A241870 Number of compositions of n such that the smallest part has multiplicity ten.

1, 0, 11, 11, 77, 143, 495, 1133, 3058, 7271, 17777, 41580, 96701, 220187, 495528, 1099626, 2412927, 5236308, 11251449, 23952841, 50556265, 105852923, 219975999, 453933348, 930544912, 1895736986, 3839424644, 7732852963, 15492659226, 30884561378, 61276442019

Offset

10,3

Comments

Conjecture: Generally, for k > 0 is column k of A238342 asymptotic to n^k * ((1+sqrt(5))/2)^(n-2*k-1) / (5^((k+1)/2) * k!). - Vaclav Kotesovec, May 02 2014

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 10..1000

Formula

a(n) ~ n^10 * ((1+sqrt(5))/2)^(n-21) / (5^(11/2) * 10!). - 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:= 10;
      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=10..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 = 10}, 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, 10, 40}] (* Jean-François Alcover, Feb 09 2015, after Maple *)

Crossrefs

Column k=10 of A238342.

Sequence in context: A003876 A014461 A111221 * A243127 A088761 A215256

Adjacent sequences: A241867 A241868 A241869 * A241871 A241872 A241873

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Apr 30 2014

Status

approved