A177995 Triangle, row sums = odd Fibonacci numbers, A014437.

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

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 n-th row terms = rightmost term of next row.

Links

Table of n, a(n) for n=1..66.

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

Cf. A014437.

Sequence in context: A257081 A271484 A199920 * A332104 A238735 A356006

Adjacent sequences: A177992 A177993 A177994 * A177996 A177997 A177998

Keyword

nonn,tabl

Author

Gary W. Adamson, May 16 2010

Status

approved