A160756 - OEIS

A160756

Triangle read by rows, infinite lower triangular Toeplitz matrix with A078008 in every column convolved with A001333.

1, 0, 1, 2, 0, 1, 2, 2, 0, 3, 6, 2, 2, 0, 7, 10, 6, 2, 6, 0, 17, 22, 10, 6, 6, 14, 0, 41, 42, 22, 10, 18, 14, 34, 0, 99, 86, 42, 22, 30, 42, 34, 82, 0, 239, 170, 86, 42, 66, 70, 102, 82, 198, 0, 577

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OFFSET

0,4

COMMENTS

Row sums = A001333: (1, 1, 3, 7, 17, 41,...). Sum of n-th row terms = rightmost term of next row.

LINKS

Table of n, a(n) for n=0..54.

FORMULA

Let M = an infinite lower triangular Toeplitz matrix with A078008 (1, 0, 2, 2, 6, 10, 22, 42, 86, 170,...). Let Q = the eigensequence of that triangle prefaced with a 1: (1, 1, 1, 3, 7, 17,...) where A001333 = (1, 1, 3, 7, 17,...). The triangle = M * Q.

EXAMPLE

First few rows of the triangle =

0, 1;

2, 0, 1;

2, 2, 0, 3;

6, 2, 2, 0, 7;

10, 6, 2, 6, 0, 17;

22, 10, 6, 6, 14, 0, 41;

42, 22, 10, 18, 14, 34, 0, 99;

86, 42, 22, 30, 42, 34, 82, 0, 239;

170, 86, 42, 66, 70, 102, 82, 198, 0, 577;

...