

A035944


Number of partitions in parts not of the form 11k, 11k+1 or 11k1. Also number of partitions with no part of size 1 and differences between parts at distance 4 are greater than 1.


0



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,4


COMMENTS

Case k=5,i=1 of Gordon Theorem.


REFERENCES

G. E. Andrews, The Theory of Partitions, AddisonWesley, 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*k2)) * (1  x^(11*k3)) * (1  x^(11*k4)) * (1  x^(11*k5)) * (1  x^(11*k6)) * (1  x^(11*k7)) * (1  x^(11*k8)) * (1  x^(11*k9)) ), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 21 2015 *)


CROSSREFS

Sequence in context: A266777 A248518 A095700 * A227134 A240013 A050366
Adjacent sequences: A035941 A035942 A035943 * A035945 A035946 A035947


KEYWORD

nonn,easy


AUTHOR

Olivier Gérard


STATUS

approved



