1,2

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.

a(n) = A000029(n) - 1 = A056342(n) + 1. Cf. A000041.

Sequence in context: A048816 A080528 A002965 this_sequence A048808 A013983 A060986

Adjacent sequences: A091693 A091694 A091695 this_sequence A091697 A091698 A091699

nonn,easy,more

N. Fernandez (primeness(AT)borve.org), Jan 29 2004