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A258002 Capped binary boundary codes for holeless strictly non-overlapping polyhexes (all orientations and rotations included). 5
1, 127, 1519, 1783, 1915, 1981, 2014, 6007, 7099, 7645, 7918, 20335, 22447, 23479, 23503, 23995, 24187, 24253, 24286, 26551, 27607, 28123, 28135, 28381, 28477, 28510, 29659, 30187, 30445, 30451, 30574, 30622, 31213, 31477, 31606, 31609, 31990, 32122, 32188, 80815, 81271, 89527, 89551, 89719, 93655, 93883, 95191, 95707, 95719, 95965, 96061 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The sequence consists of those terms of A255571 whose every A080541/A080542-rotation is also a term of A255571 and in their binary representation the number of 1's is larger than the number of 0's. More precisely, after the initial term a(0)=1 (which stands for an empty path) each term has seven more 1's than 0's in their binary representation, i.e., A037861(a(n)) = -7 for all n >= 1.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..20622; all terms up to the binary width 26+1, solutions up to 26 edges

EXAMPLE

8167737748888 is included in the sequence, as it encodes a 42-edge polyhex pattern which is composed of two seven-hex "crowns" connected by a snake-like "S-piece".

PROG

(Scheme, with Antti Karttunen's IntSeq-library)

(define A258002 (MATCHING-POS 0 1 (lambda (n) (and (negative? (A037861 n)) (isA255571? n) (isA255571? (A080542 n))))))

;; See also the code in A255571 and A080542.

CROSSREFS

Intersection of A072600 and A258001.

Intersection of A255571 and A258012.

Subsequence: A258003 (lexicographically largest representatives).

Cf. A037861.

Differs from A258012 for the first time at n=6622.

Sequence in context: A189026 A287653 A258012 * A025598 A115153 A172408

Adjacent sequences:  A257999 A258000 A258001 * A258003 A258004 A258005

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, May 16 2015

STATUS

approved

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Last modified May 24 14:36 EDT 2022. Contains 354037 sequences. (Running on oeis4.)