A222706 Total number of parts of multiplicity 6 in all partitions of n.

1, 0, 1, 1, 2, 2, 5, 5, 8, 10, 15, 18, 28, 33, 47, 58, 79, 97, 132, 161, 212, 262, 337, 414, 531, 648, 818, 1001, 1249, 1519, 1887, 2285, 2812, 3401, 4155, 5004, 6086, 7301, 8827, 10565, 12708, 15155, 18162, 21587, 25757, 30539, 36296, 42904, 50832, 59915

Offset

6,5

Links

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

Formula

G.f.: (x^6/(1-x^6)-x^7/(1-x^7))/Product_{j>0}(1-x^j).

a(n) ~ exp(Pi*sqrt(2*n/3)) / (84*Pi*sqrt(2*n)). - Vaclav Kotesovec, May 24 2018

Maple

b:= proc(n, p) option remember; `if`(n=0, [1, 0], `if`(p<1, [0, 0],
      add((l->`if`(m=6, l+[0, l[1]], l))(b(n-p*m, p-1)), m=0..n/p)))
    end:
a:= n-> b(n, n)[2]:
seq(a(n), n=6..60);

Mathematica

b[n_, p_] := b[n, p] = If[n == 0, {1, 0}, If[p < 1, {0, 0}, Sum[Function[l, If[m == 6, l + {0, l[[1]]}, l]][b[n - p*m, p - 1]], {m, 0, n/p}]]];
a[n_] := b[n, n][[2]];
Table[a[n], {n, 6, 60}] (* Jean-François Alcover, Apr 30 2018, after Alois P. Heinz *)

Crossrefs

Column k=6 of A197126.

Sequence in context: A340572 A091609 A183563 * A240495 A304393 A325535

Adjacent sequences: A222703 A222704 A222705 * A222707 A222708 A222709

Keyword

nonn

Author

Alois P. Heinz, Feb 28 2013

Status

approved