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A324015 Number of nonempty subsets of {1, ..., n} containing no two cyclically successive elements. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Cyclically successive means 1 succeeds n.
After a(1) = 1, same as A001610 shifted once to the right. Also, a(n) = A169985(n) - 1.
LINKS
FORMULA
For n <= 3, a(n) = n. Otherwise, a(n) = a(n - 1) + a(n - 2) + 1.
EXAMPLE
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}.
MATHEMATICA
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}]
CROSSREFS
Sequence in context: A363070 A023614 A001610 * A238777 A344615 A245437
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 12 2019
STATUS
approved

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Last modified March 28 15:28 EDT 2024. Contains 371254 sequences. (Running on oeis4.)