A143775 Eigentriangle of triangle A125653.

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, 75, 168, 188, 171, 144, 75, 269, 1, 269, 670, 780, 711, 624, 525, 269, 1091, 1, 1091, 2990, 3632, 3348, 2904, 2550, 2152, 1091, 4940

Offset

1,6

Comments

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:

1;

0, 2;

0, 0, 4;

0, 0, 0, 9;

0, 0, 0, 0, 24;

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

Triangle A125653 begins:

1;

1, 1;

1, 1, 1;

1, 2, 1, 1;

1, 4, 3, 1, 1;

...

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

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

Links

Table of n, a(n) for n=1..55.

Formula

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

Example

First few rows of the triangle:
  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, 75, 168, 188, 171, 144, 75, 269;
  ...
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).

Crossrefs

Cf. A125653, A125654.

Sequence in context: A347101 A240388 A049823 * A244329 A003165 A337679

Adjacent sequences: A143772 A143773 A143774 * A143776 A143777 A143778

Keyword

nonn,tabl

Author

Gary W. Adamson, Aug 31 2008

Status

approved