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A256317 Number of partitions of 4n into exactly 6 parts. 2
0, 0, 2, 11, 35, 90, 199, 391, 709, 1206, 1945, 3009, 4494, 6510, 9192, 12692, 17180, 22856, 29941, 38677, 49342, 62239, 77695, 96079, 117788, 143247, 172929, 207338, 247010, 292534, 344534, 403670, 470660, 546261, 631269, 726544, 832989, 951549, 1083239 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (3,-3,3,-6,7,-6,6,-6,7,-6,3,-3,3,-1).
FORMULA
G.f.: x^2*(x+1)^2*(x^2+1)*(x^4+2*x^3+2*x^2+x+2) / ((x-1)^6*(x^2+x+1)^2*(x^4+x^3+x^2+x+1)).
EXAMPLE
For n=2 the 2 partitions of 4*2 = 8 are [1,1,1,1,1,3] and [1,1,1,1,2,2].
MATHEMATICA
Table[Length[IntegerPartitions[4n, {6}]], {n, 0, 40}] (* or *) LinearRecurrence[ {3, -3, 3, -6, 7, -6, 6, -6, 7, -6, 3, -3, 3, -1}, {0, 0, 2, 11, 35, 90, 199, 391, 709, 1206, 1945, 3009, 4494, 6510}, 40] (* Harvey P. Dale, Apr 12 2018 *)
PROG
(PARI) concat(0, vector(40, n, k=0; forpart(p=4*n, k++, , [6, 6]); k))
(PARI) concat([0, 0], Vec(x^2*(x+1)^2*(x^2+1)*(x^4+2*x^3+2*x^2+x+2) / ((x-1)^6*(x^2+x+1)^2*(x^4+x^3+x^2+x+1)) + O(x^100)))
CROSSREFS
Cf. A238340 (4 parts), A256316 (5 parts).
Sequence in context: A041389 A205342 A000914 * A086735 A242300 A078982
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Mar 23 2015
STATUS
approved

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Last modified May 21 15:47 EDT 2024. Contains 372738 sequences. (Running on oeis4.)