A035940 - OEIS

%I #15 Jan 12 2019 20:16:08

%S 0,1,1,2,2,4,4,6,7,10,12,17,19,26,31,40,47,61,71,90,106,131,154,190,

%T 222,270,317,381,445,533,620,737,857,1011,1173,1379,1593,1863,2151,

%U 2503,2881,3343,3837,4435,5083,5853,6693,7688,8769,10043,11437,13061

%N Number of partitions in parts not of the form 9k, 9k+1 or 9k-1. Also number of partitions with no part of size 1 and differences between parts at distance 3 are greater than 1.

%C Case k=4, i=1 of Gordon Theorem.

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

%F a(n) ~ exp(2*Pi*sqrt(n)/3) / (6 * (1+2*cos(2*Pi/9)) * n^(3/4)). - _Vaclav Kotesovec_, Nov 12 2015

%p # See A035937 for GordonsTheorem

%p A035940_list := n -> GordonsTheorem([0, 1, 1, 1, 1, 1, 1, 0, 0], n):

%p A035940_list(40) # _Peter Luschny_, Jan 22 2012

%t nmax = 60; Rest[CoefficientList[Series[Product[1 / ((1 - x^(9*k-2)) * (1 - x^(9*k-3)) * (1 - x^(9*k-4)) * (1 - x^(9*k-5)) * (1 - x^(9*k-6)) * (1 - x^(9*k-7)) ), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Nov 12 2015 *)

%o (Sage) # See A035937 for GordonsTheorem

%o def A035940_list(len) :  return GordonsTheorem([0, 1, 1, 1, 1, 1, 1, 0, 0], len)

%o A035940_list(40) # _Peter Luschny_, Jan 22 2012

%K nonn,easy

%O 1,4

%A _Olivier Gérard_