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

Author

Gary W. Adamson, May 16 2010

Keywords

• nonn
• tabl

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.

Examples

			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.

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.