A241867 Number of compositions of n such that the smallest part has multiplicity seven.

1, 0, 8, 8, 44, 80, 236, 513, 1238, 2744, 6160, 13384, 28846, 61228, 128513, 266668, 548185, 1116580, 2255452, 4521198, 8998844, 17792361, 34962224, 68305274, 132724871, 256587512, 493665604, 945497642, 1803122075, 3424720416, 6479635254, 12214748337

Offset

7,3

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 7..1000

Formula

a(n) ~ n^7 * ((1+sqrt(5))/2)^(n-15) / (5^4 * 7!). - 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:= 7;
      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=7..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 = 7}, 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, 7, 40}] (* Jean-François Alcover, Feb 09 2015, after Maple *)

Crossrefs

Column k=7 of A238342.

Sequence in context: A278846 A339323 A240037 * A243124 A103744 A151782

Adjacent sequences: A241864 A241865 A241866 * A241868 A241869 A241870

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Apr 30 2014

Status

approved