A286316 Number of partitions of n with parts differing by at least two and with an odd number of parts.

0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 9, 11, 13, 15, 17, 20, 22, 25, 28, 32, 35, 40, 44, 50, 56, 63, 70, 80, 89, 101, 113, 128, 143, 162, 181, 204, 228, 256, 285, 320, 355, 396, 439, 489, 540, 599, 660, 730, 803, 886, 972, 1070, 1172, 1287, 1408, 1544, 1686, 1846, 2014, 2202, 2400, 2621, 2854, 3114, 3389, 3693, 4016, 4374, 4753, 5172, 5617, 6107, 6628, 7201, 7810

Offset

0,10

Links

Alois P. Heinz, Table of n, a(n) for n = 0..5000

Formula

a(n) = A003114(n) - A286041(n).

a(n) ~ phi^(1/2) * exp(2*Pi*sqrt(n/15)) / (4 * 3^(1/4) * 5^(1/2) * n^(3/4)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Mar 05 2020

Mathematica

Table[Length@
  Select[IntegerPartitions@n, Min[-Differences@#] > 1 && OddQ@Length@# &], {n, 80}]

Crossrefs

Cf. A003114, A286041, A039924.

Sequence in context: A091581 A014591 A286745 * A027198 A238215 A237757

Adjacent sequences: A286313 A286314 A286315 * A286317 A286318 A286319

Keyword

nonn

Author

George Beck, May 06 2017

Extensions

a(0)=0 prepended by Alois P. Heinz, May 07 2017

Status

approved