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 A256309 Number of partitions of 2n into exactly 5 parts. 2
 0, 0, 0, 1, 3, 7, 13, 23, 37, 57, 84, 119, 164, 221, 291, 377, 480, 603, 748, 918, 1115, 1342, 1602, 1898, 2233, 2611, 3034, 3507, 4033, 4616, 5260, 5969, 6747, 7599, 8529, 9542, 10642, 11835, 13125, 14518, 16019, 17633, 19366, 21224, 23212, 25337, 27604 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (2,0,-1,-1,1,0,-1,1,1,0,-2,1). FORMULA G.f.: -x^3*(x^4+x^2+x+1) / ((x-1)^5*(x+1)*(x^2+x+1)*(x^4+x^3+x^2+x+1)). EXAMPLE For n=4 the 3 partitions of 2*4 = 8 are [1,1,1,1,4], [1,1,1,2,3] and [1,1,2,2,2]. MATHEMATICA CoefficientList[Series[- x^3 (x^4 + x^2 + x + 1) / ((x - 1)^5 (x + 1) (x^2 + x + 1) (x^4 + x^3 + x^2 + x + 1)), {x, 0, 50}], x] (* Vincenzo Librandi, Mar 22 2015 *) PROG (PARI) concat(0, vector(40, n, k=0; forpart(p=2*n, k++, , [5, 5]); k)) (PARI) concat([0, 0, 0], Vec(-x^3*(x^4+x^2+x+1)/((x-1)^5*(x+1)*(x^2+x+1)*(x^4+x^3+x^2+x+1)) + O(x^100))) CROSSREFS Cf. Similar sequences: A000212 (3 parts), A001477 (2 parts), A014126 (4 parts), A256310 (6 parts). Sequence in context: A258030 A164787 A131205 * A058682 A081995 A291141 Adjacent sequences:  A256306 A256307 A256308 * A256310 A256311 A256312 KEYWORD nonn,easy AUTHOR Colin Barker, Mar 22 2015 STATUS approved

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Last modified September 25 05:14 EDT 2021. Contains 347652 sequences. (Running on oeis4.)