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%I #5 Mar 30 2012 18:50:42
%S 1,2,2,4,4,0,4,8,4,0,8,16,8,0,0,16,32,16,0,0,0,32,64,32,0,0,0,0,64,
%T 128,64,0,0,0,0,0,64,192,192,64,0,0,0,0,0,128,384,384,128,0,0,0,0,0,0,
%U 256,768,768,256,0,0,0,0,0,0,0,512,1536,1536,512,0,0,0,0,0,0,0,0,1024
%N T(n,k) = number of subsets of {1,..., n} containing exactly k squares, triangle read by rows, 0<=k<n.
%C T(n,k)=T(n, A000196(n)-k) for 0<=k<=A000196(n);
%C T(n,k)=0 iff k > A000196(n);
%C A089887(n)=T(n,0); A089889(n)=T(n,1) for n>1; A089890(n)=T(n,2) for n>2;
%C A089888(n) = Sum(T(n,k): 1<=k<=A000196(n));
%C T(n,k) = A007318(A000196(n),k)*A000079(n-A000196(n)).
%F T(n, k) = binomial(floor(n^(1/2)), k)*2^(n-floor(n^(1/2))).
%Y Cf. A000290.
%K nonn,tabl
%O 1,2
%A _Reinhard Zumkeller_, Nov 13 2003
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