OFFSET
8,5
FORMULA
a(n) = p(n)-2*p(n-1)+p(n-3)+p(n-4)-2*p(n-6)+p(n-7), where p(n) = A000041(n).
G.f.: (1-x)*Product_{k>3} 1/(1-x^k).
a(n) ~ exp(Pi*sqrt(2*n/3)) * Pi^4 / (24*sqrt(3)*n^3). - Vaclav Kotesovec, Jun 02 2018
EXAMPLE
For n = 16 we have three partitions: {[4+4+4+4], [3+3+3+3+2+2], [2+2+2+2+2+2+2+2]}, so a(16) = 3.
MAPLE
seq(combinat:-numbpart(n)-2*combinat:-numbpart(n-1)+combinat:-numbpart(n-3)+combinat:-numbpart(n-4)-2*combinat:-numbpart(n-6)+combinat:-numbpart(n-7), n=8..70)
CROSSREFS
KEYWORD
nonn
AUTHOR
Mircea Merca, Jun 11 2012
STATUS
approved