A036024 Number of partitions of n into parts not of form 4k+2, 20k, 20k+1 or 20k-1. Also number of partitions in which no odd part is repeated, with no 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.

0, 0, 1, 1, 1, 1, 2, 3, 3, 3, 5, 7, 7, 8, 12, 15, 16, 19, 24, 30, 34, 39, 49, 60, 67, 77, 95, 112, 127, 147, 175, 206, 234, 267, 315, 367, 415, 474, 553, 637, 720, 820, 945, 1082, 1223, 1384, 1585, 1807, 2032, 2294, 2612, 2957, 3321, 3738, 4229, 4770, 5344

Offset

1,7

Comments

Case k=5,i=1 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..57.

Formula

a(n) ~ exp(Pi*sqrt(2*n/5)) * sin(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+1-20))*(1 - x^(20*k- 1))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Sequence in context: A260460 A000025 A036020 * A036029 A181530 A035362

Adjacent sequences: A036021 A036022 A036023 * A036025 A036026 A036027

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved