A166309 Preliminary Wythoff Triangle, P.

1, 3, 2, 4, 6, 8, 5, 7, 9, 11, 16, 21, 10, 12, 14, 19, 24, 29, 13, 15, 17, 22, 27, 32, 37, 42, 18, 20, 25, 30, 35, 40, 45, 50, 55, 23, 28, 33, 38, 43, 48, 53, 58, 63, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 76, 34, 39, 44, 49, 54, 59, 64, 69, 74, 79, 84, 97, 110, 47, 52, 57, 62

Offset

1,2

Comments

Every positive integer occurs exactly once, so that this is a permutation of the natural numbers.

Arranging each row in increasing order results in the Wythoff triangle (A166310).

References

Clark Kimberling, "The Wythoff triangle and unique representations of positive integers," Proceedings of the Fourteenth International Conference on Fibonacci Numbers and Their Applications," Aportaciones Matematicas Invertigacion 20 (2011) 155-169.

Links

Table of n, a(n) for n=1..72.

Index entries for sequences that are permutations of the natural numbers

Formula

For a=1,2,3,... and b=0,1,...,a-1, let P(a,b) be the number of the row of the Wythoff array (A035513) that precurses to (a,b).

Example

The first six rows of P:
1
3....2
4....6...8
5....7...9..11
16..21..10..12..14
19..24..29..13..15..17
The Wythoff array W begins with
1...2...3...5...
4...7..11..18...
6..10..16..26...
These rows precurse to rows of the left-justified Wythoff array (A165357):
1...0...1...1...1...2...3...
2...1...3...4...7..11..18...
2...0...2...2...4...6..10...
P(2,0)=3 because row 3 of W precurses to (2,0).
P(2,1)=2 because row 2 of W precurses to (2,1).

Crossrefs

Cf. A035513, A165357.

Sequence in context: A254052 A371173 A105746 * A349472 A195208 A114651

Adjacent sequences: A166306 A166307 A166308 * A166310 A166311 A166312

Keyword

nonn,tabl

Author

Clark Kimberling, Oct 11 2009

Status

approved