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A102902
a(n) = 9*a(n-1) - 16*a(n-2), with a(0) = 1, a(1) = 9.
1
1, 9, 65, 441, 2929, 19305, 126881, 833049, 5467345, 35877321, 235418369, 1544728185, 10135859761, 66507086889, 436390025825, 2863396842201, 18788331166609, 123280631024265, 808912380552641, 5307721328585529
OFFSET
0,2
LINKS
R. Flórez, R. A. Higuita, and A. Mukherjee, Alternating Sums in the Hosoya Polynomial Triangle, Article 14.9.5, Journal of Integer Sequences, Vol. 17 (2014).
FORMULA
G.f.: 1/(1-9*x+16*x^2).
a(n) = Sum_{k=0..n} binomial(2*n-k+1, k)*4^k.
a(n) = Sum_{k=0..floor(n/2)} binomial(n-k, k)*(-16)^k*9^(n-2*k).
a(n) = 4^n * ChebyshevU(n, 9/8). - G. C. Greubel, Dec 09 2022
MATHEMATICA
LinearRecurrence[{9, -16}, {1, 9}, 20] (* Harvey P. Dale, Jul 28 2016 *)
PROG
(SageMath) [lucas_number1(n, 9, 16) for n in range(1, 21)] # Zerinvary Lajos, Apr 23 2009
(Magma) [4^n*Evaluate(ChebyshevSecond(n+1), 9/8): n in [0..30]]; // G. C. Greubel, Dec 09 2022
CROSSREFS
Sequence in context: A055284 A351530 A081040 * A127534 A037548 A238275
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jan 17 2005
STATUS
approved