A181651 Eigentriangle of number triangle A070909.

1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 6, 2, 2, 1, 1, 9, 3, 3, 1, 1, 1, 18, 6, 6, 2, 2, 1, 1, 27, 9, 9, 3, 3, 1, 1, 1, 54, 18, 18, 6, 6, 2, 2, 1, 1, 81, 27, 27, 9, 9, 3, 3, 1, 1, 1, 162, 54, 54, 18, 18, 6, 6, 2, 2, 1, 1

Offset

0,4

Comments

First column is (essentially) A038754. Row sums are A068911. Inverse is A181652.

Generalized (conditional) Riordan array with k-th column generated by

x^k*(1+x-x^2)/(1-3x^2) if k is even,

(1+x-2x^2-x^3)/(1-3x^2) if k is odd.

Links

Table of n, a(n) for n=0..65.

Paul Barry, Invariant number triangles, eigentriangles and Somos-4 sequences, arXiv preprint arXiv:1107.5490 [math.CO], 2011.

Example

Triangle begins
    1;
    1,  1;
    2,  1,  1;
    3,  1,  1,  1;
    6,  2,  2,  1,  1;
    9,  3,  3,  1,  1,  1;
   18,  6,  6,  2,  2,  1,  1;
   27,  9,  9,  3,  3,  1,  1,  1;
   54, 18, 18,  6,  6,  2,  2,  1,  1;
   81, 27, 27,  9,  9,  3,  3,  1,  1,  1;
  162, 54, 54, 18, 18,  6,  6,  2,  2,  1,  1;

Crossrefs

Cf. A038754, A068911, A070909, A181652.

Sequence in context: A160182 A195825 A098824 * A124032 A254046 A137457

Adjacent sequences: A181648 A181649 A181650 * A181652 A181653 A181654

Keyword

nonn,tabl

Author

Paul Barry, Nov 03 2010

Status

approved