%I #18 Jun 30 2023 01:03:39

%S 5,6,10,12,20,24,40,48,80,96,160,192,320,384,640,768,1280,1536,2560,

%T 3072,5120,6144,10240,12288,20480,24576,40960,49152,81920,98304,

%U 163840,196608,327680,393216,655360,786432,1310720,1572864,2621440,3145728

%N a(n) = 2*a(n-2) for n > 2; a(1) = 5, a(2) = 6.

%C Interleaving of A020714 and A007283 without initial term 3.

%C Partial sums are in A164096.

%C 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.

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

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

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

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

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

%t 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 *)

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

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

%K nonn

%O 1,1

%A _Klaus Brockhaus_, Aug 10 2009