A352945 a(n) = Sum_{k=0..floor(n/3)} k^(n-3*k).
1, 0, 0, 1, 1, 1, 2, 3, 5, 10, 20, 42, 93, 214, 516, 1307, 3473, 9659, 28002, 84257, 262229, 842196, 2787864, 9506796, 33388393, 120727844, 449148808, 1717595949, 6743420017, 27147152525, 111931584098, 472225684599, 2037019695797, 8979468552886, 40432306870108
Offset: 0
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..738
Programs
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PARI
a(n) = sum(k=0, n\3, k^(n-3*k));
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PARI
my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^(3*k)/(1-k*x)))
Formula
G.f.: Sum_{k>=0} x^(3*k) / (1 - k * x).
a(n) ~ sqrt(2*Pi/3) * (n/(3*LambertW(exp(1)*n/3)))^(n + 1/2 - n/LambertW(exp(1)*n/3)) / sqrt(1 + LambertW(exp(1)*n/3)). - Vaclav Kotesovec, Apr 14 2022