editing

approved

<a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0, 2).

approved

editing

(MAGMAMagma) [ n le 2 select n+4 else 2*Self(n-2): n in [1..40] ];

editing

approved

LinearRecurrence[{0, 2}, {5, 6}, 50] (* or *) With[{nn=20}, Riffle[NestList[ 2#&, 5, nn], NestList[2#&, 6, nn]]] (* Harvey P. Dale, Aug 15 2020 *)

approved

editing

a(n) = 2*a(n-2) for n > 2; a(1) = 3, 5, a(2) = 56.

3, 5, 6, 10, 12, 20, 24, 40, 48, 80, 96, 160, 192, 320, 384, 640, 768, 1280, 1536, 2560, 3072, 5120, 6144, 10240, 12288, 20480, 24576, 40960, 49152, 81920, 98304, 163840, 196608, 327680, 393216, 655360, 786432, 1310720, 1572864, 2621440, 3145728

Interleaving of A020714 and A007283 without initial term 3.

Partial sums are in A164096.

Interleaving of A020714 and A007283. The sequence comes from a bifurcation cascade into the parameter plane, exiting a chaotic window and going to another chaotic region in a system of two coupled logistic maps whose dynamical behaviour Binomial transform is A048655 without initial 1, second binomial transform is A161941 without initial 2, third binomial transform is A164037, fourth binomial transform is A161731 without initial 1, fifth binomial transform is A164038, sixth binomial transform is done in terms of their integer periodicitiesA164110.

R. O. E. Bustos-Espinoza and G. M. Ramirez-Avila. Synchronization conditions on coupled maps using periodicities, Eur. Phys. J. Special Topics, 225 (2016), 2697-2705.

Vincenzo Librandi, <a href="/A164095/b164095.txt">Table of n, a(n) for n = 1..1000</a>

A164095 with a new seeds.

a(n) = A070876(n)/3.

a(n) = (4-(-1)^n)*2^(1/4*(2*n-1+(-1)^n)).

G.f.: x*(5+6*x)/(1-2*x^2).

for n=3 the a(3)=6

for n=4 the a(4)=10

for n=5 the a(5)=12

for n=6 the a(6)=20

etc.

(MATLAB) [ n=50; a=zeros(n, 1); a(1)=3; a(2)=5;

for (MAGMA) [ n le 2 select n+4 else 2*Self(n=3-2): n, in [1..40] ];

a(n)= 2 * a(n-2);

end

a'

];

Cf. A020714 (5*2^n), A007283 (3*2^n), A164096, A048655, A161941, A164037, A161731, A164038, A164110, A070876.

Klaus Brockhaus, Aug 10 2009 ~~~

We introduced new seeds for A164095.

editing

approved

a(n) = 2*a(n-2) for n > 2; a(1) = 5, 3, a(2) = 65.

3, 5, 6, 10, 12, 20, 24, 40, 48, 80, 96, 160, 192, 320, 384, 640, 768, 1280, 1536, 2560, 3072, 5120, 6144, 10240, 12288, 20480, 24576, 40960, 49152, 81920, 98304, 163840, 196608, 327680, 393216, 655360, 786432, 1310720, 1572864, 2621440, 3145728

Interleaving of A020714 and A007283 without initial term 3. The sequence comes from a bifurcation cascade into the parameter plane, exiting a chaotic window and going to another chaotic region in a system of two coupled logistic maps whose dynamical behaviour is done in terms of their integer periodicities.

Partial sums are in A164096.

Binomial transform is A048655 without initial 1, second binomial transform is A161941 without initial 2, third binomial transform is A164037, fourth binomial transform is A161731 without initial 1, fifth binomial transform is A164038, sixth binomial transform is A164110.

R. O. E. Bustos-Espinoza and G. M. Ramirez-Avila. Synchronization conditions on coupled maps using periodicities, Eur. Phys. J. Special Topics, 225 (2016), 2697-2705.

Vincenzo Librandi, <a href="/A164095/b164095.txt">Table of n, a(n) for n = 1..1000</a>

a(n) = A070876(n)/3.

a(n) = (4-(-1)^n)*2^(1/4*(2*n-1+(-1)^n)).

G.f.: x*(5+6*x)/(1-2*x^2).

A164095 with a new seeds.

for n=3 the a(3)=6

for n=4 the a(4)=10

for n=5 the a(5)=12

for n=6 the a(6)=20

etc.

(MAGMA) [ n le 2 select n+4 else 2*Self(n-2): n in [1..40] ];

(MATLAB) [ n=50; a=zeros(n, 1); a(1)=3; a(2)=5;

for n=3:n,

a(n)= 2 * a(n-2);

end

a'

];

Cf. A020714 (5*2^n), A007283 (3*2^n), A164096, A048655, A161941, A164037, A161731, A164038, A164110, A070876.

Klaus Brockhaus, Aug 10 2009 ~~~

We introduced new seeds for A164095.

approved

editing

a(n) = 2*a(n-2) for n > 2; a(1) = 3, 5, a(2) = 56.

3, 5, 6, 10, 12, 20, 24, 40, 48, 80, 96, 160, 192, 320, 384, 640, 768, 1280, 1536, 2560, 3072, 5120, 6144, 10240, 12288, 20480, 24576, 40960, 49152, 81920, 98304, 163840, 196608, 327680, 393216, 655360, 786432, 1310720, 1572864, 2621440, 3145728

Interleaving of A020714 and A007283 without initial term 3.

Partial sums are in A164096.

Interleaving of A020714 and A007283. The sequence comes from a bifurcation cascade into the parameter plane, exiting a chaotic window and going to another chaotic region in a system of two coupled logistic maps whose dynamical behavior Binomial transform is A048655 without initial 1, second binomial transform is A161941 without initial 2, third binomial transform is A164037, fourth binomial transform is A161731 without initial 1, fifth binomial transform is A164038, sixth binomial transform is done in terms of their integer periodicitiesA164110.

R. O. E. Bustos-Espinoza and G. M. Ramirez-Avila. Synchronization conditions on coupled maps using periodicities, Eur. Phys. J. Special Topics, 225 (2016), 2697-2705.

Vincenzo Librandi, <a href="/A164095/b164095.txt">Table of n, a(n) for n = 1..1000</a>

A164095 with a new seeds: a(1)=3, a(2)=5.

a(n) = A070876(n)/3.

a(n) = (4-(-1)^n)*2^(1/4*(2*n-1+(-1)^n)).

G.f.: x*(5+6*x)/(1-2*x^2).

for n=3 the a(3)=6

for n=4 the a(4)=10

for n=5 the a(5)=12

for n=6 the a(6)=20

etc.

(MATLAB) [ n=50; a=zeros(n, 1); a(1)=3; a(2)=5;

for (MAGMA) [ n le 2 select n+4 else 2*Self(n=3-2): n, in [1..40] ];

a(n)= 2 * a(n-2);

end

a' ]

Cf. A020714 (5*2^n), A007283 (3*2^n), A164096, A048655, A161941, A164037, A161731, A164038, A164110, A070876.

~~~

Klaus Brockhaus, Aug 10 2009

We introduced new seeds for A164095.

proposed

approved

editing

proposed

a(n) = 2*a(n-2) for n > 2; a(1) = 5, 3, a(2) = 65.

3, 5, 6, 10, 12, 20, 24, 40, 48, 80, 96, 160, 192, 320, 384, 640, 768, 1280, 1536, 2560, 3072, 5120, 6144, 10240, 12288, 20480, 24576, 40960, 49152, 81920, 98304, 163840, 196608, 327680, 393216, 655360, 786432, 1310720, 1572864, 2621440, 3145728

Interleaving of A020714 and A007283 without initial term 3. The sequence comes from a bifurcation cascade into the parameter plane, exiting a chaotic window and going to another chaotic region in a system of two coupled logistic maps whose dynamical behavior is done in terms of their integer periodicities.

Partial sums are in A164096.

Binomial transform is A048655 without initial 1, second binomial transform is A161941 without initial 2, third binomial transform is A164037, fourth binomial transform is A161731 without initial 1, fifth binomial transform is A164038, sixth binomial transform is A164110.

R. O. E. Bustos-Espinoza and G. M. Ramirez-Avila. Synchronization conditions on coupled maps using periodicities, Eur. Phys. J. Special Topics, 225 (2016), 2697-2705.

Vincenzo Librandi, <a href="/A164095/b164095.txt">Table of n, a(n) for n = 1..1000</a>

A164095 with a new seeds: a(n1) = A070876(n)/3, a(2)=5.

a(n) = (4-(-1)^n)*2^(1/4*(2*n-1+(-1)^n)).

G.f.: x*(5+6*x)/(1-2*x^2).

for n=3 the a(3)=6

for n=4 the a(4)=10

for n=5 the a(5)=12

for n=6 the a(6)=20

etc.

(MAGMA) [ n le 2 select n+4 else 2*Self(n-2): n in [1..40] ];

(MATLAB) [ n=50; a=zeros(n, 1); a(1)=3; a(2)=5;

for n=3:n,

a(n)= 2 * a(n-2);

end

a' ]

Cf. A020714 (5*2^n), A007283 (3*2^n), A164096, A048655, A161941, A164037, A161731, A164038, A164110, A070876.

Klaus Brockhaus, Aug 10 2009

~~~

We introduced new seeds for A164095.

approved

editing