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A185350 Number of parts in all partitions of n in which no part occurs more than twice. 2
0, 1, 3, 3, 8, 11, 17, 23, 36, 48, 69, 88, 125, 157, 212, 271, 356, 445, 574, 711, 906, 1118, 1400, 1711, 2125, 2583, 3171, 3828, 4666, 5604, 6777, 8095, 9730, 11567, 13815, 16357, 19429, 22910, 27077, 31801, 37432, 43802, 51338, 59871, 69914, 81273, 94562 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..11410 (terms 0..1000 from Alois P. Heinz)

FORMULA

a(n) = Sum_{k>=0} k*A209318(n,k).

a(n) ~ log(3) * exp(2*Pi*sqrt(n)/3) / (2*Pi*n^(1/4)). - Vaclav Kotesovec, May 26 2018

EXAMPLE

a(6) = 17: [6], [5,1], [4,2], [3,3], [4,1,1], [3,2,1], [2,2,1,1].

a(7) = 23: [7], [6,1], [5,2], [4,3], [5,1,1], [4,2,1], [3,3,1], [3,2,2], [3,2,1,1].

MAPLE

b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(i<1, [0, 0],

      add((l->[l[1], l[2]+l[1]*j])(b(n-i*j, i-1)), j=0..min(n/i, 2))))

    end:

a:= n-> b(n, n)[2]:

seq(a(n), n=0..50);

MATHEMATICA

b[n_, i_, k_] := b[n, i, k] = If[n==0, {1, 0}, If[i<1, {0, 0}, Sum[b[n - i j, i - 1, k] /. l_List :> {l[[1]], l[[2]] + l[[1]] j}, {j, 0, Min[n/i, k]} ] ] ];

a[n_] := b[n, n, 2][[2]];

a /@ Range[0, 50] (* Jean-Fran├žois Alcover, Dec 10 2020, after Alois P. Heinz *)

CROSSREFS

Column k=2 of A210485.

Cf. A015723, A117148, A209318.

Sequence in context: A300672 A052407 A233174 * A279910 A105039 A346005

Adjacent sequences:  A185347 A185348 A185349 * A185351 A185352 A185353

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jan 21 2013

STATUS

approved

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Last modified September 22 02:48 EDT 2021. Contains 347605 sequences. (Running on oeis4.)