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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). 2

%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^(n-1).

%C 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 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 n-th sub-diagonal up to the first occurrence of (n+2)*2^(n-1), 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

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Last modified May 8 02:26 EDT 2021. Contains 343652 sequences. (Running on oeis4.)