OFFSET
0,2
COMMENTS
LINKS
Indranil Ghosh, Table of n, a(n) for n = 0..397
R. Flórez, R. A. Higuita, A. Mukherjee, Alternating Sums in the Hosoya Polynomial Triangle, Article 14.9.5 Journal of Integer Sequences, Vol. 17 (2014).
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (326, -1).
FORMULA
a(n) = 2*163*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0.
a(n) = S(n, 2*163)= U(n, 163), Chebyshev's polynomials of the second kind. See A049310.
a(n) = ((129+16*sqrt(65))^(n+1) - (129-16*sqrt(65))^(n+1))/(32*sqrt(65)), n>=0.
a(n)= sum((-1)^k*binomial(n-k, k)*326^(n-2*k), k=0..floor(n/2)), n>=0.
G.f.: 1/(1-326*x+x^2).
a(n) = ((163+18*sqrt(82))^(n+1) - (163-18*sqrt(82))^(n+1))/(36*sqrt(82)), n>=0.
MATHEMATICA
LinearRecurrence[{326, -1}, {1, 326}, 12] (* Ray Chandler, Aug 11 2015 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Aug 31 2004
STATUS
approved