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

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, 127, 201, 238, 251, 255, 256, 128, 255, 423, 520, 558, 571, 575, 576, 256, 511, 880, 1121, 1224, 1262, 1275, 1279, 1280, 512, 1023, 1815, 2391, 2656, 2760, 2798, 2811

Offset: 0

Author

Robert G. Wilson v, Jun 28 2005

Keywords

• base
• nonn
• tabf

Comments

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.

Examples

			The triangle A109435 begins
    1;
    2,   1;
    4,   3,   1;
    8,   7,   3,   1;
   16,  15,   8,   3,   1;
   32,  31,  19,   8,   3,   1;
   64,  63,  43,  20,   8,   3,   1;
  128, 127,  94,  47,  20,   8,   3,   1;
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:
   0,   0;
   1,   1;
   2,   3;
   4,   7,   8;
   8,  15,  19,  20;
  16,  31,  43,  47,  48;
  32,  63,  94, 107, 111, 112;
		

Crossrefs

Cf. A109435, A001792, A109434, A084851.

Programs

Mathematica

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}]]

Extensions

Edited by R. J. Mathar, Nov 17 2009