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A320372 Number of parts in all partitions of n with largest multiplicity two. 2
2, 0, 5, 6, 9, 13, 23, 30, 44, 58, 85, 108, 149, 191, 258, 326, 425, 532, 688, 852, 1082, 1331, 1670, 2042, 2531, 3068, 3771, 4554, 5543, 6653, 8051, 9607, 11543, 13722, 16377, 19390, 23023, 27132, 32073, 37660, 44303, 51834, 60744, 70813, 82666, 96082, 111759 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
LINKS
FORMULA
a(n) ~ log(3) * exp(2*Pi*sqrt(n)/3) / (2*Pi*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-> [0, l[1]*j]+l)(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])(2):
seq(a(n), n=2..60);
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 = 2}, (b[n, n, k] - b[n, n, k - 1])[[2]]];
a /@ Range[2, 60] (* Jean-François Alcover, Dec 13 2020, after Alois P. Heinz *)
CROSSREFS
Column k=2 of A213177.
Sequence in context: A188724 A082832 A334842 * A097709 A197877 A104555
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 11 2018
STATUS
approved

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Last modified February 25 15:54 EST 2024. Contains 370332 sequences. (Running on oeis4.)