A036032 Number of partitions of n into parts not of form 4k+2, 24k, 24k+7 or 24k-7. Also number of partitions in which no odd part is repeated, with at most 3 parts 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.

1, 1, 2, 3, 4, 5, 6, 9, 12, 14, 18, 24, 30, 36, 45, 57, 69, 83, 101, 124, 150, 177, 212, 257, 305, 358, 425, 505, 594, 694, 813, 956, 1116, 1293, 1504, 1753, 2029, 2339, 2702, 3123, 3593, 4120, 4729, 5430, 6215, 7090, 8094, 9245, 10525, 11955, 13587

Offset

1,3

Comments

Case k=6,i=4 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..51.

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 - 17))*(1 - x^(24*k - 7))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 09 2018 *)

Crossrefs

Sequence in context: A352805 A091179 A036027 * A008813 A133463 A187550

Adjacent sequences: A036029 A036030 A036031 * A036033 A036034 A036035

Keyword

nonn,easy

Author

Olivier Gérard

Extensions

Name corrected by Vaclav Kotesovec, May 09 2018

Status

approved