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A035941 Number of partitions of n into parts not of the form 9k, 9k+2 or 9k-2. Also number of partitions with 1 part of size 1 and differences between parts at distance 3 are greater than 1. 1

%I

%S 1,1,2,3,4,6,7,10,13,17,21,28,35,44,55,69,84,105,127,156,189,229,275,

%T 333,397,475,565,673,795,943,1109,1307,1533,1798,2099,2455,2855,3323,

%U 3855,4472,5169,5978,6890,7942,9132,10495,12032,13796,15778,18040

%N Number of partitions of n into parts not of the form 9k, 9k+2 or 9k-2. Also number of partitions with 1 part of size 1 and differences between parts at distance 3 are greater than 1.

%C Case k=4, i=2 of Gordon Theorem.

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

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

%p # See A035937 for GordonsTheorem

%p A035941_list := n -> GordonsTheorem([1, 0, 1, 1, 1, 1, 0, 1, 0], n):

%p A035941_list(40); # _Peter Luschny_, Jan 22 2012

%t nmax = 60; Rest[CoefficientList[Series[Product[1 / ((1 - x^(9*k-1)) * (1 - x^(9*k-3)) * (1 - x^(9*k-4)) * (1 - x^(9*k-5)) * (1 - x^(9*k-6)) * (1 - x^(9*k-8)) ), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Nov 12 2015 *)

%o (Sage) # See A035937 for GordonsTheorem

%o def A035941_list(len) : return GordonsTheorem([1, 0, 1, 1, 1, 1, 0, 1, 0], len)

%o A035941_list(40) # _Peter Luschny_, Jan 22 2012

%K nonn,easy

%O 1,3

%A _Olivier GĂ©rard_

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Last modified January 20 03:47 EST 2021. Contains 340301 sequences. (Running on oeis4.)