A241864 Number of compositions of n such that the smallest part has multiplicity four.

1, 0, 5, 5, 21, 35, 85, 175, 366, 730, 1481, 2925, 5726, 11110, 21375, 40766, 77266, 145495, 272290, 506836, 938783, 1730725, 3176920, 5808020, 10578162, 19197898, 34725765, 62616485, 112574807, 201827366, 360885835, 643679795, 1145341756, 2033369086

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

Column k=4 of A238342.

Sequence in context: A279666 A283046 A147254 * A243121 A007028 A318960

Adjacent sequences: A241861 A241862 A241863 * A241865 A241866 A241867

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Apr 30 2014

Status

approved