A256524 Number of partitions of 3n into at most 4 parts.
1, 3, 9, 18, 34, 54, 84, 120, 169, 225, 297, 378, 478, 588, 720, 864, 1033, 1215, 1425, 1650, 1906, 2178, 2484, 2808, 3169, 3549, 3969, 4410, 4894, 5400, 5952, 6528, 7153, 7803, 8505, 9234, 10018, 10830, 11700, 12600, 13561, 14553, 15609, 16698, 17854, 19044
Offset: 0
Examples
For n=1 the 3 partitions of 1*3 = 3 are [3], [1,2] and [1,1,1].
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (2,0,-2,2,-2,0,2,-1).
Programs
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Mathematica
LinearRecurrence[{2, 0, -2, 2, -2, 0, 2, -1}, {1, 3, 9, 18, 34, 54, 84, 120}, 50] (* Jean-François Alcover, Apr 26 2017 *) -
PARI
concat(1, vector(40, n, k=0; forpart(p=3*n, k++, , [1,4]); k))
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PARI
Vec((x^2+x+1)*(2*x^2+1)/((x-1)^4*(x+1)^2*(x^2+1)) + O(x^100))
Formula
G.f.: (x^2+x+1)*(2*x^2+1) / ((x-1)^4*(x+1)^2*(x^2+1)).
a(n) = A001400(3n). - Alois P. Heinz, Apr 01 2015