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A133926
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Number of equivalence classes of compositions of n into parts of size 2 and 3 under the following equivalence relation: We make a "move" by changing three consecutive 2s into two consecutive 3s or vice versa. Two compositions are equivalent if we can reach one from the other by a series of moves.
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0
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1, 1, 1, 2, 1, 3, 2, 3, 4, 3, 6, 4, 7, 7, 7, 11, 8, 14, 12, 15, 19, 16, 26, 21, 30, 32, 32, 46, 38, 57, 54, 63, 79, 71, 104, 93, 121, 134, 135, 184, 165, 226, 228, 257, 319, 301
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,4
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COMMENTS
| Sequence A133925 counts the equivalence classes with exactly one element.
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LINKS
| Problem posed on the Art of Problem Solving forum, String Replacement
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EXAMPLE
| a(5) = 2 because the two compositions 23 and 32 are inequivalent. a(6) = 1 because the two compositions 222 and 33 are equivalent.
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MATHEMATICA
| a=b=c=d=e=0; Delete[Table[z=a+b+c-e+1; a=b; b=c; c=d; d=e; e=z, {n, 100}], {{1}, {2}}] (*From Vladimir Joseph Stephan Orlovsky, Feb 27 2011*)
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CROSSREFS
| Sequence in context: A164988 A201592 A115872 * A144337 A143929 A153583
Adjacent sequences: A133923 A133924 A133925 * A133927 A133928 A133929
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KEYWORD
| hard,nonn
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AUTHOR
| Joel Lewis (jblewis(AT)post.harvard.edu), Jan 07 2008, Jan 23 2008
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