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A035974 Number of partitions of n into parts not of the form 19k, 19k+5 or 19k-5. Also number of partitions with at most 4 parts of size 1 and differences between parts at distance 8 are greater than 1. 0

%I #8 May 10 2018 03:13:07

%S 1,2,3,5,6,10,13,19,25,35,45,62,79,104,133,173,217,279,348,440,546,

%T 683,840,1043,1275,1567,1907,2328,2815,3416,4111,4957,5940,7125,8498,

%U 10148,12055,14327,16959,20075,23673,27920,32816,38562,45185,52923

%N Number of partitions of n into parts not of the form 19k, 19k+5 or 19k-5. Also number of partitions with at most 4 parts of size 1 and differences between parts at distance 8 are greater than 1.

%C Case k=9,i=5 of Gordon Theorem.

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

%F a(n) ~ exp(4*Pi*sqrt(2*n/57)) * 2^(3/4) * cos(9*Pi/38) / (3^(1/4) * 19^(3/4) * n^(3/4)). - _Vaclav Kotesovec_, May 10 2018

%t nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(19*k))*(1 - x^(19*k+ 5-19))*(1 - x^(19*k- 5))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, May 10 2018 *)

%K nonn,easy

%O 1,2

%A _Olivier GĂ©rard_

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Last modified March 19 06:32 EDT 2024. Contains 370953 sequences. (Running on oeis4.)