A155887 Riordan array (1, (1/(1-x))c(x/(1-x))), c(x) the g.f. of A000108.

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

Offset

0,5

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). - Philippe Deléham, Jan 31 2009

Links

Table of n, a(n) for n=0..61.

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).

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;
From Paul Barry, 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)

Crossrefs

Sequence in context: A245972 A088391 A128899 * A357583 A113368 A066435

Adjacent sequences: A155884 A155885 A155886 * A155888 A155889 A155890

Keyword

easy,nonn,tabl

Author

Paul Barry, Jan 29 2009

Status

approved