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 A306357 Number of nonempty subsets of {1, ..., n} containing no three cyclically successive elements. 5
 0, 1, 3, 6, 10, 20, 38, 70, 130, 240, 442, 814, 1498, 2756, 5070, 9326, 17154, 31552, 58034, 106742, 196330, 361108, 664182, 1221622, 2246914, 4132720, 7601258, 13980894, 25714874, 47297028, 86992798, 160004702, 294294530, 541292032, 995591266, 1831177830 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Cyclically successive means 1 is a successor of n. Set partitions using these subsets are counted by A323949. LINKS FORMULA For n >= 3 we have a(n) = A001644(n) - 1. From Chai Wah Wu, Jan 06 2020: (Start) a(n) = 2*a(n-1) - a(n-4) for n > 6. G.f.: x*(x^5 + x^4 - 2*x^3 + x + 1)/(x^4 - 2*x + 1). (End) EXAMPLE The a(1) = 1 through a(5) = 20 stable subsets:   {1}  {1}    {1}    {1}    {1}        {2}    {2}    {2}    {2}        {1,2}  {3}    {3}    {3}               {1,2}  {4}    {4}               {1,3}  {1,2}  {5}               {2,3}  {1,3}  {1,2}                      {1,4}  {1,3}                      {2,3}  {1,4}                      {2,4}  {1,5}                      {3,4}  {2,3}                             {2,4}                             {2,5}                             {3,4}                             {3,5}                             {4,5}                             {1,2,4}                             {1,3,4}                             {1,3,5}                             {2,3,5}                             {2,4,5} MATHEMATICA stabsubs[g_]:=Select[Rest[Subsets[Union@@g]], Select[g, Function[ed, UnsameQ@@ed&&Complement[ed, #]=={}]]=={}&]; Table[Length[stabsubs[Partition[Range[n], 3, 1, 1]]], {n, 15}] CROSSREFS Cf. A000126, A000296, A001610, A001644, A169985, A306357, A323949, A323952, A323955. Sequence in context: A295719 A178850 A018171 * A122628 A343386 A068865 Adjacent sequences:  A306354 A306355 A306356 * A306358 A306359 A306360 KEYWORD nonn AUTHOR Gus Wiseman, Feb 10 2019 STATUS approved

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Last modified December 2 16:17 EST 2021. Contains 349445 sequences. (Running on oeis4.)