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Number of partitions of n into parts not of the form 15k, 15k+7 or 15k-7. Also number of partitions with at most 6 parts of size 1 and differences between parts at distance 6 are greater than 1.

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`%I #13 May 10 2018 03:02:50
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`%S 1,1,2,3,5,7,11,14,20,27,37,48,65,83,109,139,179,225,287,357,449,556,
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`%T 691,848,1047,1276,1561,1893,2299,2772,3348,4015,4820,5756,6874,8171,
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`%U 9716,11501,13614,16058,18932,22249,26138,30613,35838,41848,48831
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`%N Number of partitions of n into parts not of the form 15k, 15k+7 or 15k-7. Also number of partitions with at most 6 parts of size 1 and differences between parts at distance 6 are greater than 1.
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`%C Case k=7,i=7 of Gordon Theorem.
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`%D G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.
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`%H Seiichi Manyama, <a href="/A035961/b035961.txt">Table of n, a(n) for n = 0..1000</a>
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`%F a(n) ~ exp(2*Pi*sqrt(2*n/15)) * 2^(1/4) * cos(Pi/30) / (15^(3/4) * n^(3/4)). - _Vaclav Kotesovec_, May 10 2018
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`%t With[ {n=30}, Series[ 1/Product[ (1 - Switch[ Mod[ k, 15 ], 0, 0, 7, 0, 8, 0, _, x^k ]), {k, 1, n} ], {x, 0, n} ] ]
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`%t nmax = 60; CoefficientList[Series[Product[(1 - x^(15*k))*(1 - x^(15*k+ 7-15))*(1 - x^(15*k- 7))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, May 10 2018 *)
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`%K nonn,easy
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`%O 0,3
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`%A _Olivier GĂ©rard_
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`%E a(0)=1 prepended by _Seiichi Manyama_, May 08 2018
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