OFFSET
0,4
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,2,2,-1,2,-1).
FORMULA
a(n) = 2*a(n-2) + 2*a(n-3) - a(n-4) + 2*a(n-5) - a(n-6).
a(n) = Sum_{k=0..floor(n/2)} binomial(2*k+1,2*n-4*k).
MATHEMATICA
CoefficientList[Series[(1-x^2+x^3)/((1-x^2+x^3)^2-4x^3), {x, 0, 40}], x] (* or *) LinearRecurrence[{0, 2, 2, -1, 2, -1}, {1, 0, 1, 3, 1, 10}, 40] (* Harvey P. Dale, Aug 11 2025 *)
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec((1-x^2+x^3)/((1-x^2+x^3)^2-4*x^3))
(PARI) a(n) = sum(k=0, n\2, binomial(2*k+1, 2*n-4*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 04 2024
STATUS
approved