A256317 Number of partitions of 4n into exactly 6 parts.
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
Offset: 0
Examples
For n=2 the 2 partitions of 4*2 = 8 are [1,1,1,1,1,3] and [1,1,1,1,2,2].
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,3,-6,7,-6,6,-6,7,-6,3,-3,3,-1).
Programs
-
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 *) -
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)))
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)).