A236603 Lowest canonical Gray cycles of length 2n.

0, 1, 0, 1, 3, 2, 0, 2, 3, 1, 5, 4, 0, 1, 3, 2, 6, 7, 5, 4, 0, 2, 3, 7, 6, 4, 5, 1, 9, 8, 0, 1, 3, 7, 5, 4, 6, 2, 10, 11, 9, 8, 0, 1, 3, 2, 6, 7, 5, 4, 12, 13, 9, 11, 10, 8, 0, 1, 3, 2, 6, 4, 5, 7, 15, 11, 9, 13, 12, 14, 10, 8, 0, 2, 3, 7, 5, 4, 6, 14, 10, 8, 12, 13, 15, 11, 9, 1, 17, 16

Offset: 1

Author

Stanislav Sykora, Feb 01 2014

Keywords

• nonn
• tabf
• hard

Comments

See A236602 for definitions regarding canonical Gray sequences (CGC). The CGC's of a given length can be sorted 'lexically'; for example, the CGC {0 1 5 4 6 7 3 2} precedes {0 1 5 7 3 2 6 4}. This sequence is then the flattened triangular table of the terms of the lowest CGC for each even length L, where L = 2*.

Note: zero unequivocally marks the start of each CGC.

Examples

			L    CGC
2    0, 1
4    0, 1, 3, 2
6    0, 2, 3, 1, 5, 4
8    0, 1, 3, 2, 6, 7, 5, 4
10   0, 2, 3, 7, 6, 4, 5, 1, 9, 8
		

Links

• Martin Ehrenstein, Table of n, a(n) for n = 1..1056 (first 306 terms from Stanislav Sykora)
• Martin Ehrenstein, Triangle for A236603 (first 17 rows from Stanislav Sykora)
• Stanislav Sykora, On Canonical Gray Cycles, Stan's Library, Vol.V, January 2014, DOI: 10.3247/SL5Math14.001

Crossrefs

Cf. A236602 (CGC counts).