A083412 Wythoff array read by rising antidiagonals.

1, 4, 2, 6, 7, 3, 9, 10, 11, 5, 12, 15, 16, 18, 8, 14, 20, 24, 26, 29, 13, 17, 23, 32, 39, 42, 47, 21, 19, 28, 37, 52, 63, 68, 76, 34, 22, 31, 45, 60, 84, 102, 110, 123, 55, 25, 36, 50, 73, 97, 136, 165, 178, 199, 89, 27, 41, 58, 81, 118, 157, 220, 267, 288, 322, 144, 30, 44

Offset: 0

Author

N. J. A. Sloane, Jun 09 2003

Keywords

• nonn
• tabl

Comments

The first term in each row is the least summand in the Zeckendorf representation of every term in the row. - Clark Kimberling, Aug 27 2008

Links

• Eric Weisstein's World of Mathematics, Wythoff Array
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

A035513 transposed. See that entry for further details.

Programs

Maple

W:= proc(n,k) Digits:= 100; (Matrix([n, floor((1+sqrt(5))/2* (n+1))]). Matrix([[0,1], [1,1]])^(k+1))[1,2] end: seq(seq(W(d-k, k), k=0..d), d=0..10); # Alois P. Heinz, Aug 18 2008

Mathematica

W[n_, k_] := Fibonacci[k + 1] Floor[n*GoldenRatio] + (n - 1) Fibonacci[k]; t = Table[ W[n - k + 1, k], {n, 12}, {k, n}] // Flatten

Extensions

More terms from Alois P. Heinz, Aug 18 2008