A335174 Herscovici's array for S_d lexicodes, read by antidiagonals.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 2, 4, 1, 1, 5, 6, 6, 5, 1, 1, 6, 7, 2, 7, 6, 1, 1, 7, 5, 16, 16, 5, 7, 1, 1, 8, 4, 17, 2, 17, 4, 8, 1, 1, 9, 13, 21, 19, 19, 21, 13, 9, 1, 1, 10, 12, 18, 26, 2, 26, 18, 12, 10, 1, 1, 11, 14, 5, 9, 27, 27, 9, 5, 14, 11, 1, 1, 12, 15, 19, 29, 58, 23, 58, 29, 19, 15, 12, 1

Offset

1,5

Comments

For the somewhat complicated definition see the Conway article.

Links

Table of n, a(n) for n=1..91.

J. H. Conway, Integral lexicographic codes, Discrete Mathematics 83.2-3 (1990): 219-235. See Table 5.

Example

The initial rows of the array are:
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1],
[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],
[1,3,2,6,7,5,4,13,12,14,15,11,10,8,9,24,25,27,26,30],
[1,4,6,2,16,17,21,18,5,19,33,32,37,38,40,15,27,127,250,256],
[1,5,7,16,2,19,26,9,29,37,95,256],
[1,6,5,17,19,2,27,58,109,138,256],
[1,7,4,21,26,27,23,256],
[1,8,13,18,9,58,256],
[1,9,12,5,29,109],
[1,10,14,19,37,138],
[1,11,15,33,95,256],
[1,12,11,32,256],
[1,13,10,37],
[1,14,8,38],
[1,15,9,40],
[1,16,24,15],
[1,17,25,27],
[1,18,27,127],
[1,19,26,250],
[1,20,30,256],
...
The initial antidiagonals are:
[1]
[1, 1]
[1, 2, 1]
[1, 3, 3, 1]
[1, 4, 2, 4, 1]
[1, 5, 6, 6, 5, 1]
[1, 6, 7, 2, 7, 6, 1]
[1, 7, 5, 16, 16, 5, 7, 1]
[1, 8, 4, 17, 2, 17, 4, 8, 1]
[1, 9, 13, 21, 19, 19, 21, 13, 9, 1]
[1, 10, 12, 18, 26, 2, 26, 18, 12, 10, 1]
...

Crossrefs

Sequence in context: A125605 A110570 A341314 * A082905 A141524 A192650

Adjacent sequences: A335171 A335172 A335173 * A335175 A335176 A335177

Keyword

nonn,tabl

Author

N. J. A. Sloane, Jun 12 2020

Status

approved