A106471 - OEIS

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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

(list; table; graph; refs; listen; history; text; internal format)

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^(2*k)/((1-2*x)*(1-x)^(2*k-2)).

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

EXAMPLE

Triangle begins

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