A256315 Number of partitions of 3n into exactly 6 parts.

0, 0, 1, 3, 11, 26, 58, 110, 199, 331, 532, 811, 1206, 1729, 2432, 3331, 4494, 5942, 7760, 9975, 12692, 15944, 19858, 24473, 29941, 36308, 43752, 52327, 62239, 73551, 86499, 101155, 117788, 136479, 157532, 181038, 207338, 236534, 269005, 304865, 344534

Offset: 0

Author

Colin Barker, Mar 23 2015

Keywords

• nonn
• easy

Comments

Also the number of partitions of 3*(n-2) into at most 6 parts. - Colin Barker, Apr 01 2015

Examples

			For n=3 the 3 partitions of 3*3 = 9 are [1,1,1,1,1,4], [1,1,1,1,2,3] and [1,1,1,2,2,2].
		

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,1,-4,2,1,-4,3,3,-4,1,2,-4,1,2,-1).

Crossrefs

Cf. A077043, A256313, A256314.

Programs

Mathematica

CoefficientList[Series[x^2*(x^8 + x^7 + 4*x^6 + 5*x^5 + 5*x^4 + 5*x^3 + 4*x^2 + x + 1)/((x - 1)^6*(x + 1)^3*(x^2 + 1)*(x^4 + x^3 + x^2 + x + 1)), {x, 0, 50}], x] (* Wesley Ivan Hurt, Feb 22 2017 *)
Table[Length@ IntegerPartitions[3 n, {6}], {n, 0, 40}] (* Michael De Vlieger, Feb 22 2017 *)

PARI

concat(0, vector(40, n, k=0; forpart(p=3*n, k++, , [6,6]); k))

PARI

concat([0,0], Vec(x^2*(x^8+x^7+4*x^6+5*x^5+5*x^4+5*x^3+4*x^2+x+1) / ((x-1)^6*(x+1)^3*(x^2+1)*(x^4+x^3+x^2+x+1)) + O(x^100)))

Formula

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