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A143964
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Sequence representing valid non-trivial 1-dimensional Hashi (a.k.a Bridges or Hashiwokakero) puzzle orientations.
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1
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0, 11, 22, 110, 121, 132, 220, 231, 242, 1100, 1210, 1221, 1232, 1320, 1331, 1342, 2200, 2310, 2321, 2332, 2420, 2431, 2442, 11000, 12100, 12210, 12221, 12232, 12320, 12331, 12342, 13200, 13310, 13321, 13332, 13420, 13431, 13442, 22000, 23100, 23210, 23221
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Contribution from Nathaniel Johnston, Sep 30 2011 (Start):
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).
For k > 1, there are 2^k-2 = A000918(k) terms in this sequence with k digits.
(End)
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LINKS
| Nathaniel Johnston, Table of n, a(n) for n = 1..10000
Wikipedia, Hashiwokakero
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MAPLE
| 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
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CROSSREFS
| Sequence in context: A111696 A047902 A081930 * A034708 A091784 A061852
Adjacent sequences: A143961 A143962 A143963 * A143965 A143966 A143967
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KEYWORD
| easy,nonn
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AUTHOR
| Edgar Almeida Ribeiro (edgar.a.ribeiro(AT)gmail.com), Sep 06 2008
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