A134564 Array read by antidiagonals: row n consists of numbers whose 4th-order Zeckendorf representation has exactly n terms.

1, 2, 6, 3, 8, 25, 4, 9, 32, 94, 5, 11, 34, 120, 344, 7, 12, 35, 127, 439, 1251, 10, 13, 42, 129, 465, 1596, 4543, 14, 15, 44, 130, 472, 1691

Offset: 1

Author

Clark Kimberling, Nov 01 2007, Dec 18 2007

Keywords

• nonn
• tabl
• more

Comments

A permutation of the positive integers.

Examples

			Northwest corner:
   1   2   3   4   5   7 10 14 19 26 36 50 69 ...
   6   8   9  11  12  13 ...
  25  32  34  35  42  44 ...
  94 120 127 129 130 156 ...
For example, 32 = 26 + 5 + 1 has 3 terms, so 32 is in row 3.
		

Links

• Clark 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. A003269, A136190, A134563.

Formula

Row 1, A035513, is the 4th-order Zeckendorf basis, b(1), b(2), b(3), .... Every positive integer has a unique 4th-order Zeckendorf representation b(i(1)) + b(i(2)) + ... + b(i(n)), where |i(h) - i(j)| >= 4 for distinct h and j.