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A256327
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Number of partitions of 5n into exactly 4 parts.
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3
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0, 1, 9, 27, 64, 120, 206, 321, 478, 672, 920, 1215, 1575, 1991, 2484, 3042, 3689, 4410, 5231, 6136, 7153, 8262, 9495, 10830, 12300, 13881, 15609, 17457, 19464, 21600, 23906, 26351, 28978, 31752, 34720, 37845, 41175, 44671, 48384, 52272, 56389, 60690, 65231
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OFFSET
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0,3
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LINKS
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Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,-2,0,0,1,1,-1).
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FORMULA
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G.f.: x*(5*x^7+13*x^6+24*x^5+29*x^4+28*x^3+17*x^2+8*x+1) / ((x-1)^4*(x+1)^2*(x^2+1)*(x^2+x+1)).
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EXAMPLE
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For n=2 the 9 partitions of 5*2 = 10 are [1,1,1,7], [1,1,2,6], [1,1,3,5], [1,1,4,4], [1,2,2,5], [1,2,3,4], [1,3,3,3], [2,2,2,4] and [2,2,3,3].
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PROG
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(PARI) concat(0, vector(40, n, k=0; forpart(p=5*n, k++, , [4, 4]); k))
(PARI) concat(0, Vec(x*(5*x^7+13*x^6+24*x^5+29*x^4+28*x^3+17*x^2+8*x+1) / ((x-1)^4*(x+1)^2*(x^2+1)*(x^2+x+1)) + O(x^100)))
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CROSSREFS
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Cf. A256328 (6n), A256329 (7n).
Sequence in context: A254622 A271990 A153237 * A011923 A029875 A129957
Adjacent sequences: A256324 A256325 A256326 * A256328 A256329 A256330
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KEYWORD
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nonn,easy
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AUTHOR
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Colin Barker, Mar 25 2015
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STATUS
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approved
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