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A222731
Total sum of parts of multiplicity 3 in all partitions of n.
2
1, 0, 1, 3, 4, 4, 11, 13, 21, 30, 44, 59, 92, 115, 165, 225, 305, 394, 546, 700, 931, 1204, 1572, 2005, 2613, 3290, 4218, 5328, 6745, 8423, 10630, 13193, 16475, 20386, 25269, 31072, 38346, 46882, 57478, 70066, 85415, 103582, 125794, 151916, 183576, 220962
OFFSET
3,4
LINKS
FORMULA
G.f.: (x^3/(1-x^3)^2-x^4/(1-x^4)^2)/Product_{i>=1}(1-x^i).
a(n) ~ 7 * sqrt(3) * exp(Pi*sqrt(2*n/3)) / (288 * Pi^2). - Vaclav Kotesovec, May 29 2018
MAPLE
b:= proc(n, p) option remember; `if`(n=0, [1, 0], `if`(p<1, [0, 0],
add((l->`if`(m=3, l+[0, l[1]*p], l))(b(n-p*m, p-1)), m=0..n/p)))
end:
a:= n-> b(n, n)[2]:
seq(a(n), n=3..50);
MATHEMATICA
b[n_, p_] := b[n, p] = If[n == 0 && p == 0, {1, 0}, If[p == 0, Array[0&, n+2], Sum[Function[l, ReplacePart[l, m+2 -> p*l[[1]] + l[[m+2]]]][Join[b[n-p*m, p-1], Array[0&, p*m]]], {m, 0, n/p}]]]; a[n_] := b[n, n][[5]]; Table[a[n], {n, 3, 50}] (* Jean-François Alcover, Jan 24 2014, after Alois P. Heinz *)
CROSSREFS
Column k=3 of A222730.
Sequence in context: A368163 A202816 A089411 * A025508 A023189 A067137
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Mar 03 2013
STATUS
approved