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%I #16 Nov 11 2022 08:06:55
%S 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,
%T 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,
%U 6,2,2,1,1
%N Eigentriangle of number triangle A070909.
%C First column is (essentially) A038754. Row sums are A068911. Inverse is A181652.
%C Generalized (conditional) Riordan array with k-th column generated by
%C x^k*(1+x-x^2)/(1-3x^2) if k is even,
%C (1+x-2x^2-x^3)/(1-3x^2) if k is odd.
%H Paul Barry, <a href="http://arxiv.org/abs/1107.5490">Invariant number triangles, eigentriangles and Somos-4 sequences</a>, arXiv preprint arXiv:1107.5490 [math.CO], 2011.
%e Triangle begins
%e 1;
%e 1, 1;
%e 2, 1, 1;
%e 3, 1, 1, 1;
%e 6, 2, 2, 1, 1;
%e 9, 3, 3, 1, 1, 1;
%e 18, 6, 6, 2, 2, 1, 1;
%e 27, 9, 9, 3, 3, 1, 1, 1;
%e 54, 18, 18, 6, 6, 2, 2, 1, 1;
%e 81, 27, 27, 9, 9, 3, 3, 1, 1, 1;
%e 162, 54, 54, 18, 18, 6, 6, 2, 2, 1, 1;
%Y Cf. A038754, A068911, A070909, A181652.
%K nonn,tabl
%O 0,4
%A _Paul Barry_, Nov 03 2010
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