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A109436 Triangle of numbers: row n gives the elements along the subdiagonal of A109435 that connects 2^n with (n+2)*2^(n-1).

%I A109436 #13 Mar 31 2024 17:24:27
%S A109436 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 A109436 127,201,238,251,255,256,128,255,423,520,558,571,575,576,256,511,880,
%U A109436 1121,1224,1262,1275,1279,1280,512,1023,1815,2391,2656,2760,2798,2811
%N A109436 Triangle of numbers: row n gives the elements along the subdiagonal of A109435 that connects 2^n with (n+2)*2^(n-1).
%C A109436 In the limit of row number n->infinity, the differences of the n-th row of the table, read from right to left, are 1, 4, 13, 38, 104,... = A084851.
%e A109436 The triangle A109435 begins
%e A109436     1;
%e A109436     2,   1;
%e A109436     4,   3,   1;
%e A109436     8,   7,   3,   1;
%e A109436    16,  15,   8,   3,   1;
%e A109436    32,  31,  19,   8,   3,   1;
%e A109436    64,  63,  43,  20,   8,   3,   1;
%e A109436   128, 127,  94,  47,  20,   8,   3,   1;
%e A109436 If we read this triangle starting at 2^n in its first column along its n-th subdiagonal up to the first occurrence of (n+2)*2^(n-1), we get row n of the current triangle, which begins:
%e A109436    0,   0;
%e A109436    1,   1;
%e A109436    2,   3;
%e A109436    4,   7,   8;
%e A109436    8,  15,  19,  20;
%e A109436   16,  31,  43,  47,  48;
%e A109436   32,  63,  94, 107, 111, 112;
%t A109436 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 A109436 Cf. A109435, A001792, A109434, A084851.
%K A109436 base,nonn,tabf
%O A109436 0,5
%A A109436 _Robert G. Wilson v_, Jun 28 2005
%E A109436 Edited by _R. J. Mathar_, Nov 17 2009