A134563 Array read by antidiagonals: row n consists of numbers whose 3rd-order Zeckendorf representation has exactly n terms.

1, 2, 5, 3, 7, 18, 4, 8, 24, 59, 6, 10, 26, 78, 188, 9, 11, 27, 84, 248, 594, 13, 12, 33, 86, 267, 783, 1872, 19, 14, 35, 87, 273, 843

Offset: 1

Author

Clark Kimberling, Nov 01 2007, Dec 18 2007

Keywords

• nonn
• tabl

Comments

A permutation of the natural numbers.

Examples

			Northwest corner of the array:
1 2 3 4 6 9 13 19 28 41 60 88 129 ...
5 7 8 10 11 12 ...
18 24 26 27 33 35 ...
59 78 84 86 87 106 ...
For example, 26=19+6+1 has 3 terms, so 26 is in row 3.
		

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. A000930, A136189, A134564.

Formula

Row 1, A000930, is the 3rd-order Zeckendorf basis, b(1), b(2), b(3), .... Every positive integer has a unique 3rd-order Zeckendorf representation b(i(1)) + b(i(2)) + ... + b(i(n)), where |i(h) - i(j)| >=3 for distinct h and j.