A140068 - OEIS

A140068

1, 1, 1, 1, 3, 1, 1, 7, 4, 1, 1, 15, 11, 6, 1, 1, 31, 26, 23, 7, 1, 1, 63, 57, 72, 30, 9, 1, 1, 127, 120, 201, 102, 48, 10, 1, 1, 255, 247, 522, 303, 198, 58, 12, 1, 1, 511, 502, 1291, 825, 699, 256, 82, 13, 1, 1, 1023, 1013, 3084, 2116, 2223, 955, 420, 95, 15, 1, 1, 2047, 2036

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OFFSET

1,5

COMMENTS

Sum of n-th row terms = odd-indexed Fibonacci numbers, F(2n+1); e.g. sum of row 5 terms = (1 + 15 + 11 + 6 + 1) = 34 = F(9).

The triangle is a companion to A140069 (having row sums = even-indexed Fibonacci numbers).

LINKS

Table of n, a(n) for n=1..69.

FORMULA

Triangle read by rows, n-th row = (n-1)-th power of the matrix X * [1,0,0,0,...] where X = an infinite lower triangular matrix with [1,2,1,2,1,2,...] in the main diagonal and [1,1,1,...] in the subdiagonal. Given the matrix X, perform X * [1,0,0,0,...] and then iterate: X * (result), etc. and record the result as each successive row of the triangle.

EXAMPLE

First few rows of the triangle are:

1, 1;

1, 3, 1;

1, 7, 4, 1;

1, 15, 11, 6, 1;

1, 31, 26, 23, 7, 1;

1, 63, 57, 72, 30, 9, 1;

1, 127, 120, 201, 102, 48, 10, 1;

1, 255, 247, 522, 303, 198, 58, 12, 1;

...

CROSSREFS