A168261 - OEIS

%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