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A320375 Number of parts in all partitions of n with largest multiplicity five. 2
5, 0, 6, 6, 13, 18, 34, 35, 66, 82, 120, 154, 230, 286, 408, 514, 699, 886, 1189, 1485, 1949, 2441, 3136, 3906, 4980, 6159, 7757, 9555, 11908, 14600, 18062, 22000, 27028, 32804, 39996, 48327, 58614, 70489, 85036, 101876, 122284, 145943, 174419, 207354, 246804 (list; graph; refs; listen; history; text; internal format)
OFFSET
5,1
LINKS
FORMULA
a(n) ~ log(6) * exp(Pi*sqrt(5*n)/3) / (2 * Pi * 5^(1/4) * n^(1/4)). - Vaclav Kotesovec, Oct 25 2018
MAPLE
b:= proc(n, i, k) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
add((l->l+[0, l[1]*j])(b(n-i*j, i-1, k)), j=0..min(n/i, k))))
end:
a:= n-> (k-> (b(n$2, k)-b(n$2, k-1))[2])(5):
seq(a(n), n=5..50);
MATHEMATICA
b[n_, i_, k_] := b[n, i, k] = If[n == 0, {1, 0}, If[i < 1, {0, 0}, Sum[Function[l, {0, l[[1]] j} + l][b[n - i j, i - 1, k]], {j, 0, Min[n/i, k]}]]];
a[n_] := With[{k = 5}, (b[n, n, k] - b[n, n, k - 1])[[2]]];
a /@ Range[5, 50] (* Jean-François Alcover, Dec 13 2020, after Alois P. Heinz *)
CROSSREFS
Column k=5 of A213177.
Sequence in context: A353876 A166126 A265011 * A361918 A200419 A271522
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 11 2018
STATUS
approved

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Last modified April 17 07:13 EDT 2024. Contains 371756 sequences. (Running on oeis4.)