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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

Table of n, a(n) for n=0..35.

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.)