A256525 Number of partitions of 3n into at most 5 parts.

1, 3, 10, 23, 47, 84, 141, 221, 333, 480, 674, 918, 1226, 1602, 2062, 2611, 3266, 4033, 4932, 5969, 7166, 8529, 10083, 11835, 13811, 16019, 18487, 21224, 24260, 27604, 31289, 35324, 39744, 44559, 49806, 55496, 61667, 68331, 75529, 83273, 91606, 100540

Offset

0,2

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,-1,-2,2,1,-2,2,0,-2,1).

Formula

G.f.: -(x^8+x^7+4*x^6+5*x^5+5*x^4+5*x^3+4*x^2+x+1) / ((x-1)^5*(x+1)^2*(x^2+1)*(x^4+x^3+x^2+x+1)).

a(n) = A001401(3n). - Alois P. Heinz, Apr 01 2015

Example

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

Mathematica

Table[Length[IntegerPartitions[3n, 5]], {n, 0, 50}] (* Harvey P. Dale, Mar 08 2019 *)

Prog

(PARI) concat(1, vector(40, n, k=0; forpart(p=3*n, k++, , [1, 5]); k))
(PARI) Vec(-(x^8+x^7+4*x^6+5*x^5+5*x^4+5*x^3+4*x^2+x+1) / ((x-1)^5*(x+1)^2*(x^2+1)*(x^4+x^3+x^2+x+1)) + O(x^100))

Crossrefs

Cf. A001401, A077043 (3 parts), A256524 (4 parts), A256315 (6 parts).

Sequence in context: A068043 A145069 A293350 * A192973 A294503 A080204

Adjacent sequences: A256522 A256523 A256524 * A256526 A256527 A256528

Keyword

nonn,easy

Author

Colin Barker, Apr 01 2015

Status

approved