A373905 - OEIS

A373905

a(n) = Sum_{k=0..floor(n/3)} binomial(n+3*k,n-3*k).

1, 1, 1, 2, 8, 29, 86, 224, 554, 1381, 3556, 9382, 24901, 65737, 172321, 450017, 1174985, 3072365, 8044478, 21074012, 55199573, 144535714, 378366976, 990441502, 2592800365, 6787973872, 17771619370, 46527959417, 121813193825, 318910531073, 834913179137

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OFFSET

0,4

LINKS

Table of n, a(n) for n=0..30.

Index entries for linear recurrences with constant coefficients, signature (6,-15,21,-15,6,-1).

FORMULA

a(n) = 6*a(n-1) - 15*a(n-2) + 21*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).

G.f.: 1/(1 - x - x^3/(1 - x)^5).

PROG

(PARI) a(n) = sum(k=0, n\3, binomial(n+3*k, n-3*k));

CROSSREFS