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A106471
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A number triangle with duplicated columns of the form 2^n-sum{j=0..2k-1, C(n,j)}.
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1
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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; internal format)
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OFFSET
| 0,2
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COMMENTS
| Columns include A000079, A000295, A002663, A035038, A035040. Row sums are A106472. Product of binomial matrix binomial(n,k) and number triangle A106465.
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FORMULA
| Column 2k has g.f. x^(2k)/((1-2x)((1-x)^2). Column 2k+1 has g.f. x^(2k+1)/((1-2x)(1-x)^2).
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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;
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CROSSREFS
| Sequence in context: A138846 A130321 A101508 * A180870 A054453 A109433
Adjacent sequences: A106468 A106469 A106470 * A106472 A106473 A106474
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 03 2005
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