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A222706 Total number of parts of multiplicity 6 in all partitions of n. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 8 14:18 EST 2021. Contains 349596 sequences. (Running on oeis4.)