OFFSET
4,3
LINKS
Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 4..1000
FORMULA
a(n) ~ (1/2-1/sqrt(5))^3 / 15 * n^4 * ((1+sqrt(5))/2)^n. - Vaclav Kotesovec, May 01 2014
MAPLE
b:= proc(n, s) option remember; `if`(n=0, 1,
`if`(n<s, 0, expand(add(b(n-j, s)*x, j=s..n))))
end:
a:= proc(n) local k; k:= 4;
add((p->add(coeff(p, x, i)*binomial(i+k, k),
i=0..degree(p)))(b(n-j*k, j+1)), j=1..n/k)
end:
seq(a(n), n=4..40);
MATHEMATICA
b[n_, s_] := b[n, s] = If[n == 0, 1, If[n<s, 0, Expand[Sum[b[n-j, s]*x, {j, s, n}]]]]; a[n_] := With[{k=4}, Sum[Function[{p}, Sum[Coefficient[p, x, i]*Binomial[i + k, k], {i, 0, Exponent[p, x]}]][b[n-j*k, j+1]], {j, 1, n/k}]]; Table[a[n], {n, 4, 40}] (* Jean-François Alcover, Feb 09 2015, after Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Joerg Arndt and Alois P. Heinz, Apr 30 2014
STATUS
approved