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A155887
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Riordan array (1, (1/(1-x))c(x/(1-x)), c(x) the g.f. of A000108.
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0
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1, 0, 1, 0, 2, 1, 0, 5, 4, 1, 0, 15, 14, 6, 1, 0, 51, 50, 27, 8, 1, 0, 188, 187, 113, 44, 10, 1, 0, 731, 730, 468, 212, 65, 12, 1, 0, 2950, 2949, 1956, 970, 355, 90, 14, 1, 0, 12235, 12234, 8291, 4356, 1785, 550, 119, 16, 1, 0, 51822, 51821, 35643, 19474, 8612, 3021
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Inverse of (1,x(1-x)/(1+x-x^2)). Row sums are A002212. Augmented version of A104259.
Triangle T(n,k) given by [0,F(3)/F(1),F(1)/F(3),F(5)/F(3),F(3)/F(5),F(7)/F(5),F(5)/F(7),...] DELTA [1,0,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938, F(n)=A000045(n) (Fibonacci numbers) . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 31 2009]
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FORMULA
| Riordan array (1, (1-sqrt((1-5x)/(1-x)))/(2x));
G.f.: 1/(1-xy/(1-x-x/(1-x/(1-x-x/(1-x/(1-x-x/(1-... (continued fraction);
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EXAMPLE
| Triangle begins
1,
0, 1,
0, 2, 1,
0, 5, 4, 1,
0, 15, 14, 6, 1,
0, 51, 50, 27, 8, 1,
0, 188, 187, 113, 44, 10, 1,
0, 731, 730, 468, 212, 65, 12, 1,
0, 2950, 2949, 1956, 970, 355, 90, 14, 1
Contribution from Paul Barry (pbarry(AT)wit.ie), Sep 28 2009: (Start)
Production matrix is
0, 1,
0, 2, 1,
0, 1, 2, 1,
0, 1, 1, 2, 1,
0, 1, 1, 1, 2, 1,
0, 1, 1, 1, 1, 2, 1,
0, 1, 1, 1, 1, 1, 2, 1,
0, 1, 1, 1, 1, 1, 1, 2, 1,
0, 1, 1, 1, 1, 1, 1, 1, 2, 1 (End)
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CROSSREFS
| Sequence in context: A060136 A088391 A128899 * A113368 A066435 A171960
Adjacent sequences: A155884 A155885 A155886 * A155888 A155889 A155890
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jan 29 2009
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