A107110 - OEIS

%I #8 Dec 02 2016 22:03:23

%S 1,0,1,0,1,1,0,0,1,1,0,0,2,1,1,0,0,1,2,1,1,0,0,1,3,2,1,1,0,0,0,3,3,2,

%T 1,1,0,0,0,3,5,3,2,1,1,0,0,0,3,5,5,3,2,1,1,0,0,0,2,7,7,5,3,2,1,1,0,0,

%U 0,1,7,9,7,5,3,2,1,1,0,0,0,1,8,11,11,7,5,3,2,1,1,0,0,0,0,7,14,13,11,7,5,3,2

%N Square array by antidiagonals where T(n,k) is the number of partitions of k into no more than n parts each no more than n. Visible version of A063746.

%H Henry Bottomley, <a href="http://www.se16.info/js/partitions.htm">Partition and composition calculator</a>.

%F See A063746 for formulas. T(n, k)=A000041(k) if n>=k. T(n, k)=T(n, n^2-k). T(n, [n^2/2])=A029895(n); T(2n, 2n^2)=A063074(n). Row sums are A000984.

%e Rows start 1,0,0,0,...; 1,1,0,0,0,...; 1,1,2,1,1,0,0,0,...; 1,1,2,3,3,3,3,2,1,1,0,0,0,...; 1,1,2,3,5,5,7,7,8,7,7,5,5,3,2,1,1,0,0,0,...; etc.

%e T(4,6)=7 since 6 can be written seven ways with no more than 4 parts each no more than 4: 4+2, 4+1+1, 3+3, 3+2+1, 3+1+1+1, 2+2+2, or 2+2+1+1.

%Y Cf. A063746. Fifth row is A102422.

%K nonn,tabl

%O 0,13

%A _Henry Bottomley_, May 12 2005