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

1,5

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*<row index>.

Note: zero unequivocally marks the start of each CGC.

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

Example

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

Crossrefs

Cf. A236602 (CGC counts).

Sequence in context: A281451 A246863 A227864 * A129576 A122861 A326045

Adjacent sequences: A236600 A236601 A236602 * A236604 A236605 A236606

Keyword

nonn,tabf,hard

Author

Stanislav Sykora, Feb 01 2014

Status

approved