A035944 Number of partitions in parts not of the form 11k, 11k+1 or 11k-1. Also number of partitions with no part of size 1 and differences between parts at distance 4 are greater than 1.

0, 1, 1, 2, 2, 4, 4, 7, 8, 11, 13, 19, 22, 30, 36, 47, 56, 73, 86, 110, 131, 163, 194, 241, 284, 348, 412, 499, 588, 709, 832, 996, 1168, 1387, 1622, 1919, 2235, 2631, 3060, 3584, 4156, 4852, 5610, 6525, 7530, 8724, 10044, 11607, 13328, 15355, 17600

Offset

1,4

Comments

Case k=5,i=1 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..51.

Formula

a(n) ~ sqrt(2) * sin(Pi/11) * 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-2)) * (1 - x^(11*k-3)) * (1 - x^(11*k-4)) * (1 - x^(11*k-5)) * (1 - x^(11*k-6)) * (1 - x^(11*k-7)) * (1 - x^(11*k-8)) * (1 - x^(11*k-9)) ), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 21 2015 *)

Crossrefs

Sequence in context: A248518 A095700 A339404 * A227134 A240013 A050366

Adjacent sequences: A035941 A035942 A035943 * A035945 A035946 A035947

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved