cp's OEIS Frontend

A110619 Triangle of number of partitions of n with no part more than n/k; also partitions of n into n/k or fewer parts.

%I A110619 #4 Mar 30 2012 18:51:39
%S A110619 1,2,1,3,1,1,5,3,1,1,7,3,1,1,1,11,7,4,1,1,1,15,8,4,1,1,1,1,22,15,5,5,
%T A110619 1,1,1,1,30,18,12,5,1,1,1,1,1,42,30,14,6,6,1,1,1,1,1,56,37,16,6,6,1,1,
%U A110619 1,1,1,1,77,58,34,19,7,7,1,1,1,1,1,1,101,71,39,21,7,7,1,1,1,1,1,1,1,135,105
%N A110619 Triangle of number of partitions of n with no part more than n/k; also partitions of n into n/k or fewer parts.
%F A110619 T(n, k)=A008284(n+floor[n/k], floor[n/k]). T(0, k)=1; T(n, k)=0 for 0<n<k; T(n, k)=1 for k<=n<2k; T(n, 1)=A000041(n); T(n, 2)=A110618(n).
%e A110619 Rows start: 1; 2,1; 3,1,1; 5,3,1,1; 7,3,1,1,1; 11,7,4,1,1,1; etc.
%e A110619 T(7,3)=4 since 7 can be partitioned as 1+1+1+1+1+1+1, 2+1+1+1+1+1, 2+2+1+1+1, or 2+2+2+1 and also as 7, 6+1, 5+2, or 4+3.
%Y A110619 First column is A000041, second is A110618.
%K A110619 nonn,tabl
%O A110619 1,2
%A A110619 _Henry Bottomley_, Aug 01 2005