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%I #14 May 04 2019 03:41:16
%S 0,11,22,110,121,132,220,231,242,1100,1210,1221,1232,1320,1331,1342,
%T 2200,2310,2321,2332,2420,2431,2442,11000,12100,12210,12221,12232,
%U 12320,12331,12342,13200,13310,13321,13332,13420,13431,13442,22000,23100,23210,23221
%N Sequence representing valid nontrivial 1-dimensional Hashi (a.k.a. Bridges or Hashiwokakero) puzzle orientations.
%C From _Nathaniel Johnston_, Sep 30 2011: (Start)
%C A k-digit number d_1 d_2 ... d_k is in this sequence if there is a multigraph with k vertices (representing the k digits) with the properties that: (1) there are at most two edges connecting d_i and d_{i+1}, and (2) there are no edges connecting d_i and d_j if i and j are not consecutive integers. In the title, "nontrivial" means that this multigraph must be connected (which eliminates terms like 1111 and 1122).
%C For k > 1, there are 2^k-2 = A000918(k) terms in this sequence with k digits.
%C (End)
%H Nathaniel Johnston, <a href="/A143964/b143964.txt">Table of n, a(n) for n = 1..10000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Hashiwokakero">Hashiwokakero</a>
%p lim:=5: L[0]:={0}: for n from 0 to lim do L[n+1]:={0,op(map(`+`,L[n],11*10^n)),op(map(`+`,L[n],22*10^n))}: od: `union`(seq(L[k],k=0..lim)); # _Nathaniel Johnston_, Sep 30 2011
%Y Cf. A000918.
%K easy,nonn
%O 1,2
%A Edgar Almeida Ribeiro (edgar.a.ribeiro(AT)gmail.com), Sep 06 2008
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