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%I #12 Mar 13 2015 18:09:45
%S 0,0,1,0,0,0,3,0,0,1,0,5,0,0,0,0,0,7,3,0,0,0,1,0,9,0,0,0,0,5,0,0,11,0,
%T 0,0,0,0,3,0,13,7,0,1,0,0,0,0,0,0,15,0,0,0,0,0,9,5,0,0,17,0,0,0,0,0,0,
%U 0,3,0,19,11,0,0,1,0,0,0,7,0,0,0,21,0
%N Triangle read by rows: T(n,k), n>=1, k>=1, in which column k lists the elements of A004273 interleaved with k zeros, and the first element of column k is in row k*(k+1)/2.
%C Alternating sum of row n equals A235796(n), i.e., sum_{k=1..A003056(n)} (-1)^(k-1)*T(n,k) = A235796(n).
%C Row n has length A003056(n) hence column k starts in row A000217(k).
%C Column k starts with k+1 zeros and then lists the odd numbers interleaved with k zeros.
%C It appears that row n lists all zeros iff n is a power of 2.
%e Triangle begins:
%e 0;
%e 0;
%e 1, 0;
%e 0, 0;
%e 3, 0;
%e 0, 1, 0;
%e 5, 0, 0;
%e 0, 0, 0;
%e 7, 3, 0;
%e 0, 0, 1, 0;
%e 9, 0, 0, 0;
%e 0, 5, 0, 0;
%e 11, 0, 0, 0;
%e 0, 0, 3, 0;
%e 13, 7, 0, 1, 0;
%e 0, 0, 0, 0, 0;
%e 15, 0, 0, 0, 0;
%e 0, 9, 5, 0, 0;
%e 17, 0, 0, 0, 0;
%e 0, 0, 0, 3, 0;
%e 19, 11, 0, 0, 1, 0;
%e 0, 0, 7, 0, 0, 0;
%e 21, 0, 0, 0, 0, 0;
%e 0, 13, 0, 0, 0, 0;
%e 23, 0, 0, 5, 0, 0;
%e ...
%e For n = 15 the 15th row of triangle is 13, 7, 0, 1, and the alternating sum is 13 - 7 + 0 - 1 = A235796(15) = 5.
%Y Cf. A000203, A000217, A003056, A004125, A004273, A196020, A231345, A231347, A235791, A235794, A235796, A236106, A236104, A236112, A237048, A237588, A237591, A239313.
%K nonn,tabf
%O 1,7
%A _Omar E. Pol_, Mar 20 2014
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