

A177995


Triangle, row sums = odd Fibonacci numbers, A014437.


1



1, 2, 1, 2, 0, 3, 2, 0, 6, 5, 2, 0, 6, 0, 13, 2, 0, 6, 0, 26, 21, 2, 0, 6, 0, 26, 0, 55, 2, 0, 6, 0, 26, 0, 110, 89, 2, 0, 6, 0, 26, 0, 110, 0, 233, 2, 0, 6, 0, 26, 0, 110, 0, 466, 377, 1, 0, 6, 0, 26, 0, 110, 0, 466, 0, 987
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OFFSET

1,2


COMMENTS

Row sums = A014437 starting (1, 3, 5, 13, 21, 55, 89, 233, 377,...). The generating triangle M (alternate columns of (1,2,2,2,...) and (1,0,0,0,...) has an eigensequence of (1, 3, 5, 13, 21, 55, 89,...); i.e., the odd Fibonacci numbers; such that M * (1, 1, 3, 5, 13,...) shifts the latter sequence to the left.
Sum of nth row terms = rightmost term of next row.


LINKS



FORMULA

Let M = an infinite lower triangular matrix with alternate columns of
(1,2,2,2,...) and (1,0,0,0,...). Let Q = A014437: (1, 1, 3, 5, 13, 21, 55,...);
diagonalized with the rest zeros. Triangle A177995 = M * Q.


EXAMPLE

First few rows of the triangle =
1;
2, 1;
2, 0, 3;
2, 0, 6, 5;
2, 0, 6, 0, 13;
2, 0, 6, 0, 26, 21;
2, 0, 6, 0, 26, 0, 55;
2, 0, 6, 0, 26, 0, 110, 89;
2, 0, 6, 0, 26, 0, 110, 0, 233;
2, 0, 6, 0, 26, 0, 110, 0, 466, 377;
2, 0, 6, 0, 26, 0, 110, 0, 466, 0, 987;
2, 0, 6, 0, 26, 0, 110, 0, 466, 0, 1974, 1597;
...


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



