A324015 Number of nonempty subsets of {1, ..., n} containing no two cyclically successive elements.

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

Offset: 0

Author

Gus Wiseman, Feb 12 2019

Keywords

• nonn

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.

Examples

			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}.
		

Crossrefs

Cf. A000045, A000126, A000296, A001610, A001644, A169985, A306357, A324014.

Programs

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}]

Formula

For n <= 3, a(n) = n. Otherwise, a(n) = a(n - 1) + a(n - 2) + 1.