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

Author

Paul Barry, Nov 03 2010

Keywords

• nonn
• tabl

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.

Examples

			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;
		

Links

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

Crossrefs

Cf. A038754, A068911, A070909, A181652.