A256226 Number of partitions of 6n into 6 parts.
0, 1, 11, 58, 199, 532, 1206, 2432, 4494, 7760, 12692, 19858, 29941, 43752, 62239, 86499, 117788, 157532, 207338, 269005, 344534, 436140, 546261, 677571, 832989, 1015691, 1229120, 1476997, 1763332, 2092435, 2468926, 2897747, 3384171, 3933815, 4552649, 5247008
Offset: 0
Examples
For n=2, the 11 partitions of 12 are Xs = [7,1,1,1,1,1], [6,2,1,1,1,1], [5,3,1,1,1,1], [4,4,1,1,1,1], [5,2,2,1,1,1], [4,3,2,1,1,1], [3,3,3,1,1,1], [4,2,2,2,1,1], [3,3,2,2,1,1], [3,2,2,2,2,1] and [2,2,2,2,2,2].
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (4,-5,0,5,-3,-3,5,0,-5,4,-1).
Programs
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Mathematica
CoefficientList[Series[x (3 x^7 + 14 x^6 + 21 x^5 + 21 x^4 + 22 x^3 + 19 x^2 + 7 x + 1) / ((x - 1)^6 (x + 1) (x^4 + x^3 + x^2 + x + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 20 2015 *) -
PARI
concat(0, Vec(x*(3*x^7+14*x^6+21*x^5+21*x^4+22*x^3+19*x^2+7*x+1)/((x-1)^6*(x+1)*(x^4+x^3+x^2+x+1)) + O(x^100)))
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PARI
concat(0, vector(35, n, k=0; forpart(p=6*n, k++, , [6,6]); k)) \\ Colin Barker, Mar 21 2015
Formula
G.f.: x*(3*x^7+14*x^6+21*x^5+21*x^4+22*x^3+19*x^2+7*x+1) / ((x-1)^6*(x+1)*(x^4+x^3+x^2+x+1)).