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A286316 Number of partitions of n with parts differing by at least two and with an odd number of parts. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 30 06:00 EDT 2022. Contains 354914 sequences. (Running on oeis4.)