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
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Apr 01 2015
STATUS
approved