A182708 a(n) is the sum of the smallest parts of all partitions of n that do not contain 1 as a part.

0, 2, 3, 6, 7, 13, 14, 23, 27, 39, 45, 67, 75, 104, 125, 165, 194, 258, 302, 392, 467, 588, 700, 885, 1045, 1296, 1546, 1897, 2249, 2753, 3252, 3945, 4670, 5616, 6633, 7957, 9357, 11157, 13124, 15573, 18257, 21599, 25259, 29760, 34760, 40788, 47526, 55642, 64669, 75465, 87576, 101898, 117991, 136977, 158286

Offset

1,2

Comments

In other words, sum of the smallest parts of all partitions of the head of the last section of the set of partitions of n.

Only one of the smallest parts is used in the sum.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Formula

a(n) = A046746(n) - A000041(n-1).

a(n) ~ Pi * exp(Pi*sqrt(2*n/3)) / (6*sqrt(2)*n^(3/2)) * (1 + (11*Pi/(24*sqrt(6)) - 3*sqrt(3/2)/Pi)/sqrt(n)). - Vaclav Kotesovec, Jan 03 2019, extended Jul 06 2019

Mathematica

Table[Total[{Min /@ IntegerPartitions[n, All, Range[2, n]]}, 2], {n, 55}] (* Robert Price, Aug 30 2020 *) (* Only suitable for n<100 *)

Prog

(PARI)  my(N=66, z='z+O('z^N));  gf=sum(k=1, N, k * z^k / prod(j=k, N, 1-z^j ) ) - z/eta(z); concat([0], Vec(gf)) \\ Joerg Arndt, Aug 31 2020

Crossrefs

Cf. A000041, A046746, A135010, A138121, A182707, A182709.

Sequence in context: A354361 A018511 A345139 * A304709 A330145 A183558

Adjacent sequences: A182705 A182706 A182707 * A182709 A182710 A182711

Keyword

nonn,easy

Author

Omar E. Pol, Nov 28 2010

Status

approved