A109434 Irregular triangle read by rows: row n contains the numbers from 2^n up to (n+3)*2^(n-2), inclusive, read along their common subdiagonal of A109433.

0, 0, 1, 1, 2, 2, 4, 5, 8, 11, 12, 16, 24, 27, 28, 32, 51, 60, 63, 64, 64, 107, 131, 140, 143, 144, 128, 222, 282, 307, 316, 319, 320, 256, 457, 601, 666, 691, 700, 703, 704, 512, 935, 1270, 1432, 1498, 1523, 1532, 1535, 1536, 1024, 1904, 2665, 3057, 3224, 3290

Offset: 0

Author

Robert G. Wilson v, Jun 28 2005

Keywords

• base
• nonn
• tabf

Comments

Evolution of 2^n into 2^(n-2)(n+3) as exhibited by A109433.

The forward differences of the last row of the table approache A058396.

Examples

			Triangle begins
   0  0
   1  1
   2  2
   4  5
   8 11 12
  16 24 27 28
  32 51 60 63 64
		

Crossrefs

Cf. A109433, A109436.

Programs

Mathematica

T[n_, m_] := Length[ Select[ StringPosition[ #, ToString[(10^m - 1)/9]] & /@ Table[ ToString[ FromDigits[ IntegerDigits[i, 2]]], {i, 2^n, 2^(n + 1) - 1}], # != {} &]]; Join[{0, 0, 1, 1, 2}, Flatten[ Table[ T[n + i, i], {n, 0, 9}, {i, n + 1}]]]

Extensions

New definition from R. J. Mathar, Nov 27 2007