A035947 Number of partitions of n into parts not of the form 11k, 11k+4 or 11k-4. Also number of partitions with at most 3 parts of size 1 and differences between parts at distance 4 are greater than 1.

1, 2, 3, 4, 6, 9, 11, 16, 21, 28, 36, 48, 60, 78, 98, 124, 154, 194, 238, 296, 362, 444, 539, 658, 793, 960, 1152, 1384, 1652, 1976, 2345, 2789, 3299, 3902, 4596, 5416, 6352, 7454, 8715, 10186, 11869, 13828, 16059, 18648, 21598, 25000, 28873, 33332

Offset

1,2

Comments

Case k=5,i=4 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(3*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-3)) * (1 - x^(11*k-5)) * (1 - x^(11*k-6)) * (1 - x^(11*k-8)) * (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: A130899 A007210 A198394 * A371839 A338914 A048249

Adjacent sequences: A035944 A035945 A035946 * A035948 A035949 A035950

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved