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%I #10 Nov 20 2022 10:52:39
%S 1,1,1,2,1,1,3,2,1,1,6,4,2,1,1,9,6,3,2,1,1,18,12,6,4,2,1,1,27,18,9,6,
%T 3,2,1,1,54,36,18,12,6,4,2,1,1,81,54,27,18,9,6,3,2,1,1,162,108,54,36,
%U 18,12,6,4,2,1,1
%N An eigentriangle of the number triangle A181653.
%C Generalized (conditional) Riordan array with k-th column generated by x^k*if(mod(k,2)=0,(1+x-x^2)/(1-3x^2),(1+x-x^2+x^3)/(1-3x^2)).
%C Row sums are A181655.
%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, 2, 1, 1,
%e 6, 4, 2, 1, 1,
%e 9, 6, 3, 2, 1, 1,
%e 18, 12, 6, 4, 2, 1, 1,
%e 27, 18, 9, 6, 3, 2, 1, 1,
%e 54, 36, 18, 12, 6, 4, 2, 1, 1,
%e 81, 54, 27, 18, 9, 6, 3, 2, 1, 1,
%e 162, 108, 54, 36, 18, 12, 6, 4, 2, 1, 1
%K easy,nonn,tabl
%O 0,4
%A _Paul Barry_, Nov 03 2010
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