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*(2*x^2+3*x+2)^2 / ((x-1)^3*(x+1)*(x^2+x+1)).
EXAMPLE
For n=1 the 4 partitions of 7*1 = 7 are [1, 1, 5], [1, 2, 4], [1, 3, 3] and [2, 2, 3].
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 *)
PROG
(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)))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Mar 24 2015
STATUS
approved