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A256310 Number of partitions of 2n into exactly 6 parts. 2
0, 0, 0, 1, 2, 5, 11, 20, 35, 58, 90, 136, 199, 282, 391, 532, 709, 931, 1206, 1540, 1945, 2432, 3009, 3692, 4494, 5427, 6510, 7760, 9192, 10829, 12692, 14800, 17180, 19858, 22856, 26207, 29941, 34085, 38677, 43752, 49342, 55491, 62239, 69624, 77695, 86499 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The number of partitions of 2*(n-3) into at most 6 parts. - Colin Barker, Mar 31 2015

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,0,0,-3,1,1,0,0,1,1,-3,0,0,2,-1).

FORMULA

G.f.: x^3*(x^4+x^3+x^2+1) / ((x-1)^6*(x+1)*(x^2+x+1)^2*(x^4+x^3+x^2+x+1)).

EXAMPLE

For n=4 the 2 partitions of 2*4 = 8 are [1,1,1,1,1,3] and [1,1,1,1,2,2].

MATHEMATICA

CoefficientList[Series[x^3 (x^4 + x^3 + x^2 + 1) / ((x - 1)^6 (x + 1) (x^2 + x + 1)^2 (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++, , [6, 6]); k))

(PARI) concat([0, 0, 0], Vec(x^3*(x^4+x^3+x^2+1)/((x-1)^6*(x+1)*(x^2+x+1)^2*(x^4+x^3+x^2+x+1)) + O(x^100)))

CROSSREFS

Cf. Similar sequences: A000212 (3 parts), A001477 (2 parts), A014126 (4 parts), A256309 (5 parts).

Sequence in context: A038377 A261227 A022908 * A026390 A005575 A294745

Adjacent sequences:  A256307 A256308 A256309 * A256311 A256312 A256313

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Mar 22 2015

STATUS

approved

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Last modified October 15 21:06 EDT 2018. Contains 316237 sequences. (Running on oeis4.)