OFFSET
0,8
LINKS
Ludovic Schwob, Table of n, a(n) for n = 0..10000
FORMULA
G.f.: Product_{k>=1} 1/((1 - x^(7*k))*(1 - x^(7*k-2))*(1 - x^(7*k-5))).
a(n) = a(n-2) + a(n-5) - a(n-11) - a(n-17) + + - - (with a(0)=1 and a(n) = 0 for negative n), where 2, 5, 11, 17, ... is the sequence A274830.
a(n) ~ exp(Pi*sqrt(2*n/7)) / (8*cos(3*Pi/14)*n). - Vaclav Kotesovec, Aug 05 2021
EXAMPLE
For n=17 the a(17)=6 solutions are 2+2+2+2+2+2+5, 2+2+2+2+2+7, 2+2+2+2+9, 2+5+5+5, 5+5+7 and 5+12.
MATHEMATICA
CoefficientList[Series[Product[1/((1 - x^(7*k))(1 - x^(7*k-2))(1 - x^(7*k-5))), {k, 52}], {x, 0, 52}], x] (* Stefano Spezia, Aug 04 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ludovic Schwob, Aug 04 2021
STATUS
approved