A256322 Number of partitions of 7n into exactly 3 parts.

0, 4, 16, 37, 65, 102, 147, 200, 261, 331, 408, 494, 588, 690, 800, 919, 1045, 1180, 1323, 1474, 1633, 1801, 1976, 2160, 2352, 2552, 2760, 2977, 3201, 3434, 3675, 3924, 4181, 4447, 4720, 5002, 5292, 5590, 5896, 6211, 6533, 6864, 7203, 7550, 7905, 8269, 8640

Offset: 0

Author

Colin Barker, Mar 24 2015

Keywords

• nonn
• easy

Examples

			For n=1 the 4 partitions of 7*1 = 7 are [1, 1, 5], [1, 2, 4], [1, 3, 3] and [2, 2, 3].
		

Links

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

Crossrefs

Cf. A033428 (6n), A256320 (4n), A256321 (5n).

Programs

Mathematica

Length /@ (Total /@ IntegerPartitions[7 #, {3}] & /@ Range[0, 46]) (* Michael De Vlieger, Mar 24 2015 *)
LinearRecurrence[{1,1,0,-1,-1,1},{0,4,16,37,65,102},50] (* Harvey P. Dale, Aug 29 2024 *)

PARI

concat(0, vector(40, n, k=0; forpart(p=7*n, k++, , [3,3]); k))

PARI

concat(0, Vec(-x*(2*x^2+3*x+2)^2/((x-1)^3*(x+1)*(x^2+x+1)) + O(x^100)))

Formula

a(n) = a(n-1)+a(n-2)-a(n-4)-a(n-5)+a(n-6) for n>5.

G.f.: -x*(2*x^2+3*x+2)^2 / ((x-1)^3*(x+1)*(x^2+x+1)).