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
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Mar 24 2015
STATUS
approved