A036030 Number of partitions of n into parts not of form 4k+2, 24k, 24k+3 or 24k-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 5 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, 43, 50, 60, 75, 90, 105, 125, 152, 181, 210, 247, 295, 347, 402, 469, 553, 645, 743, 861, 1004, 1162, 1333, 1535, 1776, 2042, 2332, 2670, 3067, 3507, 3989, 4545, 5190, 5905, 6691, 7589, 8621, 9765

Offset

1,4

Comments

Case k=6,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..53.

Formula

a(n) ~ 5^(1/4) * (3 - 2*sqrt(2))^(1/4) * exp(sqrt(5*n/3)*Pi/2) / (2^(11/4) * 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 - 21))*(1 - x^(24*k - 3))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 09 2018 *)

Crossrefs

Sequence in context: A365831 A036021 A036025 * A036022 A036026 A116494

Adjacent sequences: A036027 A036028 A036029 * A036031 A036032 A036033

Keyword

nonn,easy

Author

Olivier Gérard

Extensions

Name corrected by Vaclav Kotesovec, May 09 2018

Status

approved