A134570 Array T(n,k) by antidiagonals; T(n,k) = position in row n of k-th occurrence of the Fibonacci number F(2n+1) in A134566.

2, 5, 1, 7, 4, 3, 10, 6, 11, 8, 13, 9, 16, 29, 21, 15, 12, 24, 42, 76, 55, 18, 14, 32, 63, 110, 199, 144, 20, 17, 37, 84, 165, 288, 521, 377, 23, 19, 45, 97, 220, 432, 754

Offset: 1

Author

Clark Kimberling, Nov 02 2007

Keywords

• nonn
• tabl

Comments

(Row 1) = A001950, the upper Wythoff sequence (Row 2) = (Column 1 of Wythoff array) = A003622 (Row 3) = (Column 3 of Wythoff array) = A035337 (Row 4) = (Column 5 of Wythoff array) = A035339 Except for initial terms, the first two columns of A134570 are bisected Fibonacci and Lucas sequences, A001906 and A002878, resp. Row 1 is the ordered union of all even-numbered columns of the Wythoff array; and A134570 is a permutation of the positive integers.

Examples

			Northwest corner:
2 5 7 10 13 15 18 20 23 26
1 4 6 9 12 14
3 11 16 24 32 37
8 29 42 63 84 97
Row 1 consists of numbers k such that 1 is the least m for which {-m*tau}>{k*tau}, where tau=(1+sqrt(5))/2 and {} denotes fractional part.
		

Crossrefs

Cf. A134566, A134571.