A036029 Number of partitions of n into parts not of form 4k+2, 24k, 24k+1 or 24k-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 5 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, 25, 31, 35, 40, 50, 62, 69, 80, 99, 117, 133, 154, 184, 217, 247, 283, 335, 391, 443, 507, 593, 685, 776, 886, 1024, 1175, 1331, 1510, 1733, 1980, 2232, 2526, 2883, 3271, 3682, 4154, 4710, 5324

Offset

1,7

Comments

Case k=6,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..56.

Formula

a(n) ~ 5^(1/4) * sqrt(2 - sqrt(2 + sqrt(3))) * exp(sqrt(5*n/3)*Pi/2) / (8 * 3^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 09 2018

Mathematica

nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(4*k - 2))*(1 - x^(24*k))*(1 - x^(24*k - 23))*(1 - x^(24*k - 1))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 09 2018 *)

Crossrefs

Sequence in context: A000025 A036020 A036024 * A181530 A035362 A042957

Adjacent sequences: A036026 A036027 A036028 * A036030 A036031 A036032

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved