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%I #7 Jan 22 2023 08:37:31
%S 1,1,1,0,0,2,1,1,0,2,0,0,0,0,4,0,0,2,0,0,4,0,0,0,0,0,0,6,1,1,0,2,0,0,
%T 0,6,0,0,0,0,0,0,0,0,10,0,0,0,0,4,0,0,0,0,10,0,0,0,0,0,0,0,0,0,0,14,0,
%U 0,2,0,0,4,0,0,0,0,0,14,0,0,0,0,0,0,0,0,0,0,0,0,20
%N Triangle read by rows, A115361 * the diagonalized variant of A018819.
%C Row sums = A018819 starting with offset 1; (1, 2, 2, 4, 4, 6, 6, 10, 10,...).
%C Equals the eigensequence of triangle A115361.
%C Rightmost diagonal = A018819.
%C Sum of n-th row terms = rightmost term of next row.
%F Equals M*Q as infinite lower triangular matrices, where M = triangle A115361, and Q = the diagonalized variant of A018819 such that (1, 1, 2, 2, 4, 4, 6, 6,...) = rightmost diagonal with the rest zeros.
%e First few rows of the triangle =
%e 1;
%e 1, 1;
%e 0, 0, 2;
%e 1, 1, 0, 2;
%e 0, 0, 0, 0, 4;
%e 0, 0, 2, 0, 0, 4;
%e 0, 0, 0, 0, 0 0, 6;
%e 1, 1, 0, 2, 0, 0, 0, 6;
%e 0, 0, 0, 0, 0, 0, 0, 0, 10;
%e 0, 0, 0, 0, 4, 0, 0, 0, 0, 10;
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14;
%e 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 14;
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20;
%e 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 20;
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26;
%e 1, 1, 0, 2, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 26;
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36;
%e ...
%Y Cf. A115361, A018819.
%K nonn,tabl
%O 1,6
%A _Gary W. Adamson_, Nov 21 2009
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