A143775 - OEIS

%I #7 May 04 2024 09:24:20

%S 1,1,1,1,1,2,1,2,2,4,1,4,6,4,9,1,9,16,16,9,24,1,24,48,52,45,24,75,1,

%T 75,168,188,171,144,75,269,1,269,670,780,711,624,525,269,1091,1,1091,

%U 2990,3632,3348,2904,2550,2152,1091,4940

%N Eigentriangle of triangle A125653.

%C An eigentriangle of triangle T is generated by taking the termwise product row (n-1) of T and the first n terms of the eigensequence of T. Here T = A125653 and the eigensequence of T = A125654. The operation (A125654 * 0^(n-k)) creates an infinite lower triangular matrix with A125654 as the main diagonal and the rest zeros:

%C   1;

%C   0, 2;

%C   0, 0, 4;

%C   0, 0, 0, 9;

%C   0, 0, 0, 0, 24;

%C   ..., where A125654 = (1, 1, 2, 4, 9, 24, 75, 269,...).

%C Triangle A125653 begins:

%C   1;

%C   1, 1;

%C   1, 1, 1;

%C   1, 2, 1, 1;

%C   1, 4, 3, 1, 1;

%C   ...

%C Row sums = A125654 (column 1) shifted one place to the left: (1, 2, 4, 9, 24, 75,...).

%C Sum of row n terms = rightmost term of row (n+1).

%F Triangle read by rows, A125653 * (A125654 * 0^(n-k)); 0<=k<=n

%e First few rows of the triangle:

%e   1;

%e   1, 1;

%e   1, 1, 2;

%e   1, 2, 2, 4;

%e   1, 4, 6, 4, 9;

%e   1, 9, 16, 16, 9, 24;

%e   1, 24, 48, 52, 45, 24, 75;

%e   1, 75, 168, 188, 171, 144, 75, 269;

%e   ...

%e Row 4 = (1, 4, 6, 4, 9) = termwise product of row 4 of triangle A143775: (1, 4, 3, 1, 1) and the first 5 terms of A125654: (1, 1, 2, 4, 9) = (1*1, 4*1, 3*2, 1*4, 1*9).

%Y Cf. A125653, A125654.

%K nonn,tabl

%O 1,6

%A _Gary W. Adamson_, Aug 31 2008