A106471 A number triangle with duplicated columns of the form 2^n - Sum_{j=0..2k-1} C(n,j).

1, 2, 1, 4, 2, 1, 8, 4, 4, 1, 16, 8, 11, 4, 1, 32, 16, 26, 11, 6, 1, 64, 32, 57, 26, 22, 6, 1, 128, 64, 120, 57, 64, 22, 8, 1, 256, 128, 247, 120, 163, 64, 37, 8, 1, 512, 256, 502, 247, 382, 163, 130, 37, 10, 1, 1024, 512, 1013, 502, 848, 382, 386, 130, 56, 10, 1, 2048, 1024

Offset

0,2

Comments

Columns include A000079, A000295, A002663, A035038, A035040.

Row sums are A106472.

Product of binomial matrix binomial(n,k) and number triangle A106465.

Links

Table of n, a(n) for n=0..67.

Formula

Column 2k has g.f. x^(2k)/((1-2x)((1-x)^(2k-2)).

Column 2k+1 has g.f. x^(2k+1)/((1-2x)(1-x)^(2k)).

Example

Triangle begins
   1;
   2,  1;
   4,  2,  1;
   8,  4,  4,  1;
  16,  8, 11,  4,  1;
  32, 16, 26, 11,  6, 1;
  64, 32, 57, 26, 22, 6, 1;

Crossrefs

Sequence in context: A235670 A130321 A101508 * A180870 A228565 A054453

Adjacent sequences: A106468 A106469 A106470 * A106472 A106473 A106474

Keyword

easy,nonn,tabl

Author

Paul Barry, May 03 2005

Status

approved