OFFSET
0,2
LINKS
Indranil Ghosh, Table of n, a(n) for n = 0..1221
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).
Index entries for linear recurrences with constant coefficients, signature (9,-16).
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
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jan 17 2005
STATUS
approved