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A376648
a(n) = Sum_{k=0..floor(n/4)} binomial(floor(k/2),n-4*k).
1
1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 3, 3, 1, 1, 3, 3, 1, 1, 4, 6, 4, 2, 4, 6, 4, 2, 5, 10, 10, 6, 6, 10, 10, 6, 7, 15, 20, 16, 12, 16, 20, 16, 13, 22, 35, 36, 28, 28, 36, 36, 29, 35, 57, 71, 64, 56, 64, 72, 65, 64, 92, 128, 135
OFFSET
0,18
FORMULA
G.f.: (1-x^8)/((1-x^4) * (1-x^8-x^9)) = (1+x^4)/(1-x^8-x^9).
a(n) = a(n-8) + a(n-9).
a(n) = A017867(n) + A017867(n-4).
PROG
(PARI) a(n) = sum(k=0, n\4, binomial(k\2, n-4*k));
(PARI) my(N=80, x='x+O('x^N)); Vec((1+x^4)/(1-x^8-x^9))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Oct 01 2024
STATUS
approved