A241865 Number of compositions of n such that the smallest part has multiplicity five.

1, 0, 6, 6, 27, 49, 125, 258, 579, 1202, 2512, 5157, 10463, 20949, 41627, 81912, 159834, 309641, 595836, 1139211, 2165502, 4094219, 7701857, 14420351, 26880988, 49902183, 92279657, 170020844, 312173822, 571307477, 1042310911, 1896039086, 3439404321, 6222483152

Offset

5,3

Links

Joerg Arndt, Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 5..1500 (first 1000 terms from Joerg Arndt and Alois P. Heinz)

Formula

a(n) ~ n^5 * ((1+sqrt(5))/2)^(n-11) / (5^3 * 5!). - Vaclav Kotesovec, May 02 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:= 5;
      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=5..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 = 5}, 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, 5, 40}] (* Jean-François Alcover, Feb 09 2015, after Maple *)

Crossrefs

Column k=5 of A238342.

Sequence in context: A286482 A123874 A339321 * A243122 A274940 A341548

Adjacent sequences: A241862 A241863 A241864 * A241866 A241867 A241868

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Apr 30 2014

Status

approved