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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
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
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
KEYWORD
base,nonn
AUTHOR
Eric Angelini and Carole Dubois, Feb 07 2022
STATUS
approved