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A241866 Number of compositions of n such that the smallest part has multiplicity six. 2
1, 0, 7, 7, 35, 63, 176, 371, 861, 1862, 4032, 8512, 17851, 36848, 75286, 152334, 305466, 607313, 1198443, 2348388, 4571728, 8846314, 17021480, 32579029, 62048589, 117627699, 222018034, 417326148, 781395064, 1457684326, 2709797693, 5020734691, 9273107977 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,3

LINKS

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 6..1000

FORMULA

a(n) ~ n^6 * ((1+sqrt(5))/2)^(n-13) / (5^(7/2) * 6!). - 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:= 6;

      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=6..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 = 6}, 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, 6, 40}] (* Jean-Fran├žois Alcover, Feb 09 2015, after Maple *)

CROSSREFS

Column k=6 of A238342.

Sequence in context: A286862 A290683 A121210 * A243123 A154702 A112685

Adjacent sequences:  A241863 A241864 A241865 * A241867 A241868 A241869

KEYWORD

nonn

AUTHOR

Joerg Arndt and Alois P. Heinz, Apr 30 2014

STATUS

approved

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Last modified January 18 11:33 EST 2019. Contains 319271 sequences. (Running on oeis4.)