%I
%S 0,0,1,1,2,3,4,7,8,8,15,19,20,16,31,43,47,48,32,63,94,107,111,112,64,
%T 127,201,238,251,255,256,128,255,423,520,558,571,575,576,256,511,880,
%U 1121,1224,1262,1275,1279,1280,512,1023,1815,2391,2656,2760,2798,2811
%N Triangle of numbers: row n gives the elements along the subdiagonal of A109435 that connects 2^n with (n+2)*2^(n1).
%C In the limit of row number n>infinity, the differences of the nth row of the table, read from right to left, are 1, 4, 13, 38, 104,... = A084851.
%e The triangle A109435 begins
%e 1;
%e 2, 1;
%e 4, 3, 1;
%e 8, 7, 3, 1;
%e 16, 15, 8, 3, 1;
%e 32, 31, 19, 8, 3, 1;
%e 64, 63, 43, 20, 8, 3, 1;
%e 128, 127, 94, 47, 20, 8, 3, 1;
%e If we read this triangle starting at 2^n in its first column along its nth subdiagonal up to the first occurrence of (n+2)*2^(n1), we get row n of the current triangle, which begins:
%e 0, 0;
%e 1, 1;
%e 2, 3;
%e 4, 7, 8;
%e 8, 15, 19, 20;
%e 16, 31, 43, 47, 48;
%e 32, 63, 94, 107, 111, 112;
%t T[n_, m_] := Length[ Select[ StringPosition[ #, StringDrop[ ToString[10^m], 1]] & /@ Table[ ToString[ FromDigits[ IntegerDigits[i, 2]]], {i, 2^n, 2^(n + 1)  1}], # != {} &]]; Flatten[ Table[ T[n + i, i], {n, 0, 9}, {i, 0, n}]]
%Y Cf. A109435, A001792, A109434, A084851.
%K base,nonn,tabf
%O 0,5
%A _Robert G. Wilson v_, Jun 28 2005
%E Edited by _R. J. Mathar_, Nov 17 2009
