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A256313
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Number of partitions of 3n into exactly 4 parts.
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3
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0, 0, 2, 6, 15, 27, 47, 72, 108, 150, 206, 270, 351, 441, 551, 672, 816, 972, 1154, 1350, 1575, 1815, 2087, 2376, 2700, 3042, 3422, 3822, 4263, 4725, 5231, 5760, 6336, 6936, 7586, 8262, 8991, 9747, 10559, 11400, 12300, 13230, 14222, 15246, 16335, 17457
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: x^2*(x^2+2)*(x^2+x+1) / ((x-1)^4*(x+1)^2*(x^2+1)).
a(n) = (6*n^3+6*n^2-3*n-5+(3*n+1)*(-1)^n+2*((-1)^((2*n-1+(-1)^n)/4)+(-1)^((2*n+1-(-1)^n)/4)))/32. - Luce ETIENNE, Feb 17 2017
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EXAMPLE
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For n=3 the 6 partitions of 3*3 = 9 are [1,1,1,6], [1,1,2,5], [1,1,3,4], [1,2,2,4], [1,2,3,3] and [2,2,2,3].
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MATHEMATICA
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LinearRecurrence[{2, 0, -2, 2, -2, 0, 2, -1}, {0, 0, 2, 6, 15, 27, 47, 72}, 60] (* Harvey P. Dale, Jul 18 2021 *)
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PROG
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(PARI) concat(0, vector(40, n, k=0; forpart(p=3*n, k++, , [4, 4]); k))
(PARI) concat([0, 0], Vec(x^2*(x^2+2)*(x^2+x+1)/((x-1)^4*(x+1)^2*(x^2+1)) + O(x^100)))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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