A036025 Number of partitions of n into parts not of form 4k+2, 20k, 20k+3 or 20k-3. Also number of partitions in which no odd part is repeated, with 1 part of size less than or equal to 2 and where differences between parts at distance 4 are greater than 1 when the smallest part is odd and greater than 2 when the smallest part is even.

1, 1, 1, 2, 3, 3, 4, 6, 8, 9, 11, 15, 19, 22, 27, 35, 42, 49, 59, 73, 88, 102, 121, 147, 174, 202, 237, 282, 331, 382, 445, 523, 608, 699, 808, 940, 1085, 1241, 1426, 1646, 1887, 2150, 2456, 2814, 3210, 3642, 4140, 4717, 5353, 6051, 6848, 7761, 8770, 9879

Offset

1,4

Comments

Case k=5,i=2 of Gordon/Goellnitz/Andrews Theorem.

References

G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 114.

Links

Table of n, a(n) for n=1..54.

Formula

a(n) ~ exp(Pi*sqrt(2*n/5)) * sin(3*Pi/20) / (10^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018

Mathematica

nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(4*k - 2))*(1 - x^(20*k))*(1 - x^(20*k+3-20))*(1 - x^(20*k- 3))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A341144 A365831 A036021 * A036030 A036022 A036026

Adjacent sequences: A036022 A036023 A036024 * A036026 A036027 A036028

Keyword

nonn,easy

Author

Olivier Gérard

Extensions

Name corrected by Vaclav Kotesovec, May 09 2018

Status

approved