A134561 Array T by antidiagonals: T(n,k) = k-th number whose Zeckendorf representation has exactly n terms.

1, 2, 4, 3, 6, 12, 5, 7, 17, 33, 8, 9, 19, 46, 88, 13, 10, 20, 51, 122, 232, 21, 11, 25, 53, 135, 321, 609, 34, 14, 27, 54, 140, 355, 842, 1596, 55, 15, 28, 67, 142, 368, 931, 2206, 4180, 89, 16, 30, 72, 143, 373, 965

Offset: 1

Author

Clark Kimberling, Nov 01 2007

Keywords

• nonn
• tabl

Comments

A permutation of the natural numbers.

Except for initial terms in some cases, (Row 1) = A000045 (Row 2) = A095096 (Row 3) = A059390 (Row 4) = A111458 (Col 1) = A027941 (Col 2) = A005592.

Examples

			19 = 13 + 5 + 1 is the 3rd-largest number (after 12 and 17) that has a 3-term Zeckendorf representation; i.e., the (unique) sum of distinct non-neighboring Fibonacci numbers.
Northwest corner:
1 2 3 5 8 13
4 6 7 9 10 11
12 17 19 20 25 27
33 46 51 53 54 67
		

Links

• C. Kimberling, The Zeckendorf array equals the Wythoff array, Fibonacci Quarterly 33 (1995) 3-8.
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A035513.