A035945 Number of partitions of n into parts not of the form 11k, 11k+2 or 11k-2. Also number of partitions with 1 part of size 1 and differences between parts at distance 4 are greater than 1.

1, 1, 2, 3, 4, 6, 8, 11, 14, 19, 24, 32, 40, 51, 65, 82, 101, 127, 156, 193, 236, 289, 350, 427, 514, 620, 744, 893, 1064, 1271, 1508, 1790, 2116, 2500, 2942, 3464, 4060, 4758, 5560, 6494, 7560, 8801, 10216, 11852, 13720, 15870, 18317, 21133, 24328

Offset

1,3

Comments

Case k=5,i=2 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..49.

Formula

a(n) ~ sin(2*Pi/11) * 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-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-10)) ), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 21 2015 *)

Crossrefs

Sequence in context: A003412 A038348 A239467 * A094707 A353864 A303663

Adjacent sequences: A035942 A035943 A035944 * A035946 A035947 A035948

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved