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 A325786 Number of complete necklace compositions of n. 5
 1, 1, 2, 2, 4, 7, 12, 19, 41, 71, 141, 255, 509, 924, 1882, 3395, 6838, 12715, 25233, 47049 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A necklace composition of n is a finite sequence of positive integers summing to n that is lexicographically minimal among all of its cyclic rotations. A circular subsequence is a sequence of consecutive terms where the first and last parts are also considered consecutive. A necklace composition of n is complete if every positive integer from 1 to n is the sum of some circular subsequence. LINKS Table of n, a(n) for n=1..20. EXAMPLE The a(1) = 1 through a(8) = 19 necklace compositions: (1) (11) (12) (112) (113) (123) (124) (1124) (111) (1111) (122) (132) (142) (1133) (1112) (1113) (1114) (1142) (11111) (1122) (1123) (1214) (1212) (1132) (1223) (11112) (1213) (1322) (111111) (1222) (11114) (11113) (11123) (11122) (11132) (11212) (11213) (111112) (11222) (1111111) (11312) (12122) (111113) (111122) (111212) (112112) (1111112) (11111111) MATHEMATICA neckQ[q_]:=Array[OrderedQ[{q, RotateRight[q, #]}]&, Length[q]-1, 1, And]; subalt[q_]:=Union[ReplaceList[q, {___, s__, ___}:>{s}], DeleteCases[ReplaceList[q, {t___, __, u___}:>{u, t}], {}]]; Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], neckQ[#]&&Union[Total/@subalt[#]]==Range[n]&]], {n, 15}] CROSSREFS Cf. A000740, A002033, A008965, A103295, A108917, A126796, A276024, A325549, A325682, A325781, A325788, A325789, A325791. Sequence in context: A000983 A095325 A179183 * A244457 A325908 A153970 Adjacent sequences: A325783 A325784 A325785 * A325787 A325788 A325789 KEYWORD nonn,more AUTHOR Gus Wiseman, May 22 2019 STATUS approved

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Last modified June 14 08:50 EDT 2024. Contains 373393 sequences. (Running on oeis4.)