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Search: id:A166309
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| A166309 |
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Preliminary Wythoff Triangle, P. |
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+0
2
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| 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
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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(1) Every positive integer occurs exactly once, so that this is a
permutation of the natural numbers.
(2) Arranging each row in increasing order results in the Wythoff
triangle (A166310).
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REFERENCES
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Clark Kimberling, "The Wythoff triangle and unique representations of positive integers," preprint, 2009.
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FORMULA
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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).
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EXAMPLE
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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 (A1653576):
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).
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CROSSREFS
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Cf. A035513, A165357.
Sequence in context: A021312 A099258 A105746 this_sequence A114651 A138245 A163328
Adjacent sequences: A166306 A166307 A166308 this_sequence A166310 A166311 A166312
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Oct 11 2009
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