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A070936 Square array read by antidiagonals: T(n,k) = number of partitions of n into distinct parts, each no more than k.

%I A070936 #18 Oct 26 2017 08:54:52
%S A070936 1,1,0,1,1,0,1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,1,1,1,2,0,0,0,1,1,1,2,1,0,
%T A070936 0,0,1,1,1,2,2,1,0,0,0,1,1,1,2,2,2,1,0,0,0,1,1,1,2,2,3,2,0,0,0,0,1,1,
%U A070936 1,2,2,3,3,2,0,0,0,0,1,1,1,2,2,3,4,3,1,0,0,0,0,1,1,1,2,2,3,4,4,3,1,0,0,0,0
%N A070936 Square array read by antidiagonals: T(n,k) = number of partitions of n into distinct parts, each no more than k.
%H A070936 Seiichi Manyama, <a href="/A070936/b070936.txt">Antidiagonals n = 0..139, flattened</a>
%H A070936 Henry Bottomley, <a href="http://www.se16.info/js/partitions.htm">Partition calculators using java applets</a>
%H A070936 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A070936 T(n, k) =T(n-1, k)+T(n-1, k-n) (with T(0, 0)=1) =A053632(k, n) =A026836(n+k+1, k+1) =sum_{0<=j<=k}A026836(n, j). For k>=n, T(n, k)=T(n, n)=A000009(n).
%e A070936 Rows start
%e A070936 1,1,1,1,1,...;
%e A070936 0,1,1,1,1,...;
%e A070936 0,0,1,1,1,...;
%e A070936 0,0,1,2,2,...;
%e A070936 0,0,0,1,2,...; etc.
%e A070936 T(10,5)=3 since 10 can be partitioned 3 ways as 5+4+1=5+3+2=4+3+2+1 with each part less than or equal to 5.
%Y A070936 Cf. A008284, A060016. With some imagination, this is the transpose of A026836 and A053632. Column sums are 2^k=A000079(k). Column maximum is A025591(k), which appears A070936(k) times in the column.
%K A070936 nonn,tabl,look
%O A070936 0,25
%A A070936 _Henry Bottomley_, May 12 2002