A035946 Number of partitions in parts not of the form 11k, 11k+3 or 11k-3. Also number of partitions with at most 2 parts of size 1 and differences between parts at distance 4 are greater than 1.

1, 2, 2, 4, 5, 8, 10, 14, 18, 25, 31, 42, 52, 68, 84, 108, 133, 168, 205, 256, 311, 384, 463, 567, 681, 826, 988, 1190, 1416, 1696, 2009, 2392, 2823, 3344, 3931, 4636, 5431, 6376, 7445, 8708, 10135, 11812, 13706, 15920, 18423, 21332, 24618, 28424

Offset

1,2

Comments

Case k=5,i=3 of Gordon Theorem.

References

G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.

Links

Table of n, a(n) for n=1..48.

Formula

a(n) ~ cos(5*Pi/22) * sqrt(2) * exp(4*Pi*sqrt(n/33)) / (3^(1/4) * 11^(3/4) * n^(3/4)). - Vaclav Kotesovec, Nov 21 2015

Mathematica

nmax = 60; Rest[CoefficientList[Series[Product[1 / ((1 - x^(11*k-1)) * (1 - x^(11*k-2)) * (1 - x^(11*k-4)) * (1 - x^(11*k-5)) * (1 - x^(11*k-6)) * (1 - x^(11*k-7)) * (1 - x^(11*k-9)) * (1 - x^(11*k-10)) ), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 21 2015 *)

Crossrefs

Sequence in context: A331443 A367411 A367684 * A303939 A326446 A323530

Adjacent sequences: A035943 A035944 A035945 * A035947 A035948 A035949

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved