OFFSET
1,7
COMMENTS
Also number of partitions of n such that if the largest part is k, then k-1 occurs exactly once and k-2 also occurs (0 is considered to be a part of each partition). Example: a(11)=5 because we have [4,3,2,2], [4,3,2,1,1], [3,3,2,1,1,1], [2,2,2,2,2,1] and [3,2,1,1,1,1,1,1].
FORMULA
G.f.: sum(x^(2k+1)/product(1-x^j, j=k+2..infinity), k=1..infinity). G.f.: sum(x^(3k-3)/[(1-x^k)*product(1-x^j, j=1..k-2)], k=2..infinity).
a(n) = -p(n+4)+2*p(n+3)-p(n+1)-p(n-1)+p(n-2), where p(n) = A000041(n). - Mircea Merca, Jul 10 2013
EXAMPLE
a(11)=5 because we have [8,2,1], [6,5], [6,3,2], [5,3,2,1] and [4,4,2,1].
MAPLE
g:=sum(x^(3*k-3)/(1-x^k)/product(1-x^j, j=1..k-2), k=2..30): gser:=series(g, x, 65): seq(coeff(gser, x, n), n=1..62);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Apr 20 2006
STATUS
approved