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A258002 Capped binary boundary codes for holeless strictly non-overlapping polyhexes (all orientations and rotations included).

%I A258002 #16 Jul 06 2015 23:40:25
%S A258002 1,127,1519,1783,1915,1981,2014,6007,7099,7645,7918,20335,22447,23479,
%T A258002 23503,23995,24187,24253,24286,26551,27607,28123,28135,28381,28477,
%U A258002 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
%N A258002 Capped binary boundary codes for holeless strictly non-overlapping polyhexes (all orientations and rotations included).
%C A258002 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.
%H A258002 Antti Karttunen, <a href="/A258002/b258002.txt">Table of n, a(n) for n = 0..20622; all terms up to the binary width 26+1, solutions up to 26 edges</a>
%e A258002 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".
%o A258002 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A258002 (define A258002 (MATCHING-POS 0 1 (lambda (n) (and (negative? (A037861 n)) (isA255571? n) (isA255571? (A080542 n))))))
%o A258002 ;; See also the code in A255571 and A080542.
%Y A258002 Intersection of A072600 and A258001.
%Y A258002 Intersection of A255571 and A258012.
%Y A258002 Subsequence: A258003 (lexicographically largest representatives).
%Y A258002 Cf. A037861.
%Y A258002 Differs from A258012 for the first time at n=6622.
%K A258002 nonn,base
%O A258002 0,2
%A A258002 _Antti Karttunen_, May 16 2015