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Search: id:A048248
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| A048248 |
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Possible traces of n-step walks on 1-D lattice, ignoring translations. |
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+0
1
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| 1, 2, 4, 7, 14, 23, 45, 72, 137, 217, 402, 635, 1149, 1816, 3221, 5101, 8898, 14127, 24305, 38688, 65809
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Translations discounted, so the sequence of visits <0,1,2,1,0> has trace (2,2), as do <0,-1,0,1,0>, <0,-1,-2,-1,0>, etc.
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EXAMPLE
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a(4)=7 since a walk of 4 steps can leave traces (1,1,1,1), (1,1,2), (2,1,1), (2,2), (1,3), (3,1) and (4). Note that (1,2,1) is impossible.
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MATHEMATICA
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For[size = 1, size < 10, size++, traces = {}; For[i = 0, i < 2^ size, i++, thePath = IntegerDigits[i, 2, size]*2 - 1; loc = size + 2; theTrace = Table[0, {z, -size - 1, size + 1}]; For[j = 1, j <= size, j++, loc += thePath[[j]]; If[thePath[[j]] == 1, theTrace[[loc - 1]]++, theTrace[[loc]]++ ]; ]; theTrace = Select[theTrace, # > 0 &]; If[ ! MemberQ[traces, theTrace], traces = Append[traces, theTrace]]; ]; Print[Length[traces]]]; - Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 17 2006
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CROSSREFS
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Sequence in context: A054160 A034426 A000075 this_sequence A056180 A000076 A054169
Adjacent sequences: A048245 A048246 A048247 this_sequence A048249 A048250 A048251
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KEYWORD
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nonn,more
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AUTHOR
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Tony Bartoletti (azb(AT)home.com)
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EXTENSIONS
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More terms from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 17 2006
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