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A143775 Eigentriangle of triangle A125653. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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 A143775 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).

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).

LINKS

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

FORMULA

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

CROSSREFS

A125653, Cf. 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

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Last modified December 6 22:42 EST 2021. Contains 349567 sequences. (Running on oeis4.)