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

Author

Eric Angelini and Carole Dubois, Feb 07 2022

Keywords

• base
• nonn

Examples

			[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.
		

Links

• Carole Dubois, Table of n, a(n) for n = 1..1002
• Eric Angelini, More Manhattan distinct distances, Feb. 7th, 2022, personal blog.

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).