OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..4000
Index entries for linear recurrences with constant coefficients, signature (4,-6,3).
FORMULA
a(n) = Sum_{k=0..floor(n/3)} (-1)^k*binomial(n+3,3*k+3).
a(n) = 4*a(n-1) - 6*a(n-2) + 3*a(n-3) for n > 2.
a(6*n) = 1.
a(n) = 1 - A057681(n+3). - Yomna Bakr and Greg Dresden, Apr 22 2024
MATHEMATICA
LinearRecurrence[{4, -6, 3}, {1, 4, 10}, 38] (* Amiram Eldar, May 13 2021 *)
PROG
(PARI) {a(n) = sum(k=0, n\3, (-1)^k*binomial(n+3, 3*k+3))}
(PARI) N=66; x='x+O('x^N); Vec(1/((1-x)*((1-x)^3+x^3)))
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Seiichi Manyama, Apr 07 2019
STATUS
approved