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Search: id:A084084
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| A084084 |
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Length of lists created by n substitutions k -> Range[0,1+Mod[k+1,3]] starting with {0}. |
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+0
1
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| 1, 3, 9, 28, 86, 265, 816, 2513, 7739, 23833, 73396, 226030, 696081, 2143648, 6601569, 20330163, 62608681, 192809420, 593775046, 1828587033, 5631308624, 17342153393, 53406819691, 164471408185, 506505428836, 1559831901918
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Transformation invert T109 gave a match with A078039; T100 binomial gave a match with A012781; equivalent to replacements 0->{0,1,2}; 1->{0,1,2,3}; 2->{0,1}, 3->{0,1,2} operating n times with {0}.
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FORMULA
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G.f.: -(-1-x)/(1-2x-3x^2-x^3)
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EXAMPLE
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{0}, {0,1,2}, {0,1,2,0,1,2,3,0,1}, {0,1,2,0,1,2,3,0,1,0,1,2,0,1,2,3,0,1,0,1,2,0,1,2,0,1,2,3} have lengths 1, 3, 9, 28.
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MATHEMATICA
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Length/@Flatten/@NestList[ # /. k_Integer:>Range[0, 1+Mod[k+1, 3]]&, {0}, 8]
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CROSSREFS
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Cf. A078039, A012781.
Adjacent sequences: A084081 A084082 A084083 this_sequence A084085 A084086 A084087
Sequence in context: A027090 A033139 A005354 this_sequence A091140 A052541 A024738
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KEYWORD
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nonn
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be), May 11 2003
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