A351298 Concatenation of the lexicographically earliest 6-term closed circuits formed on a square grid by distinct segments of length a(n) at right angle.

1, 2, 3, 5, 4, 7, 6, 8, 9, 10, 15, 18, 11, 12, 13, 14, 24, 26, 16, 17, 19, 20, 35, 37, 21, 22, 23, 25, 44, 47, 27, 28, 29, 30, 56, 58, 31, 32, 33, 34, 64, 66, 36, 38, 39, 40, 75, 78, 41, 42, 43, 45, 84, 87, 46, 48, 49, 50, 95, 98, 51, 52, 53, 54, 104, 106, 55, 57, 59, 60, 114, 117, 61, 62, 63, 65, 124, 127, 67

Offset

1,2

Links

Carole Dubois, Table of n, a(n) for n = 1..1002

Eric Angelini, More Manhattan distinct distances, Feb. 7th, 2022, personal blog.

Example

[1, 2, 3, 5, 4, 7]  is a closed circuit on a square grid formed by going 1 cell up (North), 2 cells to the right (East), 3 cells up again (North), 5 cells to the right again (East), 4 cells down (South) and 7 cells to the left (West); the next smallest such circuit is given by [6, 8, 9, 10, 15, 18] as all the terms of the final sequence must be distinct; the next circuit is [11, 12, 13, 14, 24, 26], etc. Concatenating all circuits gives the sequence.

Crossrefs

Cf. A101544 (where the array has 3 columns; there are 6 columns here: if we label them a, b, c, d, e, f the terms a + c = e and b + d = f).

Sequence in context: A340477 A340401 A160051 * A082746 A098313 A098311

Adjacent sequences: A351295 A351296 A351297 * A351299 A351300 A351301

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Feb 07 2022

Status

approved