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A324015
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Number of nonempty subsets of {1, ..., n} containing no two cyclically successive elements.
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5
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0, 1, 2, 3, 6, 10, 17, 28, 46, 75, 122, 198, 321, 520, 842, 1363, 2206, 3570, 5777, 9348, 15126, 24475, 39602, 64078, 103681, 167760, 271442, 439203, 710646, 1149850, 1860497, 3010348, 4870846, 7881195, 12752042, 20633238, 33385281, 54018520, 87403802
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OFFSET
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0,3
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COMMENTS
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Cyclically successive means 1 succeeds n.
After a(1) = 1, same as A001610 shifted once to the right. Also, a(n) = A169985(n) - 1.
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LINKS
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FORMULA
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For n <= 3, a(n) = n. Otherwise, a(n) = a(n - 1) + a(n - 2) + 1.
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EXAMPLE
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The a(6) = 17 stable subsets:
{1}, {2}, {3}, {4}, {5}, {6},
{1,3}, {1,4}, {1,5}, {2,4}, {2,5}, {2,6}, {3,5}, {3,6}, {4,6},
{1,3,5}, {2,4,6}.
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MATHEMATICA
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stabsubs[g_]:=Select[Rest[Subsets[Union@@g]], Select[g, Function[ed, UnsameQ@@ed&&Complement[ed, #]=={}]]=={}&];
Table[Length[stabsubs[Partition[Range[n], 2, 1, 1]]], {n, 0, 10}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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