A256321 Number of partitions of 5n into exactly 3 parts.

0, 2, 8, 19, 33, 52, 75, 102, 133, 169, 208, 252, 300, 352, 408, 469, 533, 602, 675, 752, 833, 919, 1008, 1102, 1200, 1302, 1408, 1519, 1633, 1752, 1875, 2002, 2133, 2269, 2408, 2552, 2700, 2852, 3008, 3169, 3333, 3502, 3675, 3852, 4033, 4219, 4408, 4602

Offset

0,2

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).

Formula

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

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

Example

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

Mathematica

Length /@ (Total /@ IntegerPartitions[5 #, {3}] & /@ Range[0, 47]) (* Michael De Vlieger, Mar 24 2015 *)
LinearRecurrence[{1, 1, 0, -1, -1, 1}, {0, 2, 8, 19, 33, 52}, 50] (* Harvey P. Dale, Oct 29 2017 *)

Prog

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

Crossrefs

Cf. A033428 (6n), A256320 (4n), A256322 (7n).

Sequence in context: A236327 A109071 A196134 * A192136 A031327 A193389

Adjacent sequences: A256318 A256319 A256320 * A256322 A256323 A256324

Keyword

nonn,easy

Author

Colin Barker, Mar 24 2015

Status

approved