A373640 a(n) = Sum_{k=0..floor(n/3)} binomial(3*n-8*k,k).
1, 1, 1, 2, 5, 8, 12, 24, 45, 76, 134, 246, 440, 775, 1386, 2490, 4437, 7902, 14128, 25248, 45042, 80396, 143604, 256410, 457704, 817209, 1459215, 2605267, 4651330, 8304787, 14827872, 26473839, 47266965, 84392484, 150677220, 269022969, 480322072, 857583545
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (1,0,3,0,0,-3,0,0,1).
Programs
-
PARI
a(n) = sum(k=0, n\3, binomial(3*n-8*k, k));
Formula
G.f.: 1 / (1 - x^3 - x/(1 - x^3)^2).
a(n) = a(n-1) + 3*a(n-3) - 3*a(n-6) + a(n-9) for n > 8.