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A091696
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Number of classes of compositions of n equivalent under reflection or cycling.
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2
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1, 2, 3, 5, 7, 12, 17, 29, 45, 77, 125, 223, 379, 686, 1223, 2249, 4111, 7684, 14309, 27011, 50963, 96908, 184409, 352697, 675187, 1296857, 2493725, 4806077, 9272779, 17920859, 34669601, 67159049, 130216123, 252745367, 490984487, 954637557
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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EXAMPLE
| 7 has 15 partitions and 64 compositions. Compositions can -> other compositions by reflection, cycling, or both, e.g. {1,2,4} -> {4,2,1} (reflection), {2,4,1} (cycling), or {1,4,2} (both). The no. of equivalence classes so defined is 2 greater than the no. of partitions because only {3,1,2,1} and {2,1,2,1,1} (and their equivalents) cannot -> the conventionally stated forms of partitions (here, {3,2,1,1} and {2,2,1,1,1} respectively). So a(7) = 15 + 2 = 17.
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CROSSREFS
| a(n) = A000029(n) - 1 = A056342(n) + 1. Cf. A000041.
Sequence in context: A206788 A002965 A206290 * A048808 A013983 A169986
Adjacent sequences: A091693 A091694 A091695 * A091697 A091698 A091699
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KEYWORD
| nonn,easy,changed
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AUTHOR
| N. Fernandez (primeness(AT)borve.org), Jan 29 2004
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EXTENSIONS
| More terms from Sean A. Irvine (sairvin(AT)xtra.co.nz), Feb 09 2012
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