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A256328
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Number of partitions of 6n into exactly 4 parts.
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3
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0, 2, 15, 47, 108, 206, 351, 551, 816, 1154, 1575, 2087, 2700, 3422, 4263, 5231, 6336, 7586, 8991, 10559, 12300, 14222, 16335, 18647, 21168, 23906, 26871, 30071, 33516, 37214, 41175, 45407, 49920, 54722, 59823, 65231, 70956, 77006, 83391, 90119, 97200
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OFFSET
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0,2
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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 (3,-2,-2,3,-1).
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FORMULA
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a(n) = (-1+(-1)^n+6*n^2+12*n^3)/8.
a(n) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5) for n>4.
G.f.: x*(x+2)*(x^2+4*x+1) / ((x-1)^4*(x+1)).
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EXAMPLE
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For n=1 the 2 partitions of 6*1 = 6 are [1,1,1,3] and [1,1,2,2].
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PROG
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(PARI) concat(0, vector(40, n, k=0; forpart(p=6*n, k++, , [4, 4]); k))
(PARI) concat(0, Vec(x*(x+2)*(x^2+4*x+1)/((x-1)^4*(x+1)) + O(x^100)))
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CROSSREFS
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Cf. A256327 (5n), A256329 (7n).
Sequence in context: A152015 A162256 A229013 * A041719 A133777 A025213
Adjacent sequences: A256325 A256326 A256327 * A256329 A256330 A256331
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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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