Search: id:A110619
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%I A110619
%S A110619 1,2,1,3,1,1,5,3,1,1,7,3,1,1,1,11,7,4,1,1,1,15,8,4,1,1,1,1,22,15,5,5,1,
%T A110619 1,1,1,30,18,12,5,1,1,1,1,1,42,30,14,6,6,1,1,1,1,1,56,37,16,6,6,1,1,1,
               1,
%U A110619 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.
%Y A110619 Sequence in context: A160183 A026807 A106740 this_sequence A129761 A156248 
               A123864
%Y A110619 Adjacent sequences: A110616 A110617 A110618 this_sequence A110620 A110621 
               A110622
%K A110619 nonn,tabl
%O A110619 1,2
%A A110619 Henry Bottomley (se16(AT)btinternet.com), Aug 01 2005

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