STATUS
proposed
approved
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Revision History for A084131
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STATUS
editing
proposed
NAME
a(n) =10a 10*a(n-1) -17a 17*a(n-2), a(0) =0, 1, a(1) = 5.
LINKS
G. C. Greubel, <a href="/A084131/b084131.txt">Table of n, a(n) for n = 0..1000</a>
FORMULA
a(n) = (5+sqrt(8))^n/2 + (5-sqrt(8))^n/2; G.f.: (1-5x)/(1-10x+17x^2); E.g.f.: exp(5x)cosh(sqrt(8)x).
G.f.: (1-5*x)/(1-10*x+17*x^2).
E.g.f.: exp(5*x)*cosh(sqrt(8)*x).
a(n) = 17^((n-1)/2)*( sqrt(17)*ChebyshevU(n, 5/sqrt(17)) - 5*ChebyshevU(n-1, 5/sqrt(17)) ). - G. C. Greubel, Oct 13 2022
PROG
(Magma) [n le 2 select 5^(n-1) else 10*Self(n-1) -17*Self(n-2): n in [1..41]]; // G. C. Greubel, Oct 13 2022
(SageMath)
A084131=BinaryRecurrenceSequence(10, -17, 1, 5)
[A084131(n) for n in range(41)] # G. C. Greubel, Oct 13 2022
CROSSREFS
Cf. A084130.
STATUS
approved
editing
STATUS
editing
approved
LINKS
<a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-17).
MATHEMATICA
LinearRecurrence[{10, -17}, {1, 5}, 20] (* Harvey P. Dale, Apr 04 2021 *)
STATUS
approved
editing
AUTHOR
_Paul Barry (pbarry(AT)wit.ie), _, May 16 2003
FORMULA
a(n)=(5+sqrt(8))^n/2+(5-sqrt(8))^n/2; G.f. : (1-5x)/(1-10x+17x^2); E.g.f.: exp(5x)cosh(sqrt(8)x).
KEYWORD
easy,nonn,new
NAME
a(n)=10a(n-1)-17a(n-2), a(0)=0,a(1)=5.
DATA
1, 5, 33, 245, 1889, 14725, 115137, 901045, 7053121, 55213445, 432231393, 3383685365, 26488919969, 207366548485, 1623353845377, 12708307129525, 99486055923841, 778819338036485, 6096930429659553, 47729375549975285
OFFSET
0,2
COMMENTS
Binomial transform of A084130.
FORMULA
a(n)=(5+sqrt(8))^n/2+(5-sqrt(8))^n/2; G.f. : (1-5x)/(1-10x+17x^2); E.g.f.: exp(5x)cosh(sqrt(8)x).
KEYWORD
easy,nonn
AUTHOR
Paul Barry (pbarry(AT)wit.ie), May 16 2003
STATUS
approved