A256195 -id:A256195 - cp's OEIS frontend

A256202 Number of permutations in S_n that avoid the pattern 53241.

1, 1, 2, 6, 24, 119, 694, 4580, 33256, 260370, 2166120, 18945144, 172810050, 1633997788, 15939893003, 159820729208, 1641980432159, 17242378256155, 184674461615836, 2013829450204384, 22324460502429244, 251250502143635615, 2867467023751687892, 33152272498223444540

Offset: 0

N. J. A. Sloane, Mar 19 2015

nonn

Anthony Guttmann, Table of n, a(n) for n = 0..26
Nathan Clisby, Andrew R. Conway, Anthony J. Guttmann, Yuma Inoue, Classical length-5 pattern-avoiding permutations, arXiv:2109.13485 [math.CO], 2021.
Zvezdelina Stankova-Frenkel and Julian West, A new class of Wilf-equivalent permutations, arXiv:math/0103152 [math.CO], 2001.

Representatives for the 16 Wilf-equivalence patterns of length 5 are given in A116485, A047889, and A256195-A256208.

Cf. A099952.

avoid[n_, pat_] := Module[{p1 = pat[[1]], p2 = pat[[2]], p3 = pat[[3]], p4 = pat[[4]], p5 = pat[[5]], lseq = {}, i, p,
    lpat = Subsets[(n + 1) - Range[n], {Length[pat]}],
    psn = Permutations[Range[n]]},
   For[i = 1, i <= Length[lpat], i++,
    p = lpat[[i]];
    AppendTo[lseq, Select[psn, MemberQ[#, {_, p[[p1]], _, p[[p2]], _, p[[p3]], _, p[[p4]], _, p[[p5]], _}, {0}] &]];
    ]; n! - Length[Union[Flatten[lseq, 1]]]];
Table[avoid[n, {5, 3, 2, 4, 1}], {n, 0, 8}]  (* Robert Price, Mar 27 2020 *)

More terms from Anthony Guttmann, Sep 29 2021

A256203 Number of permutations in S_n that avoid the pattern 43251.

Original entry on oeis.org

1, 1, 2, 6, 24, 119, 694, 4581, 33283, 260805, 2171393, 18994464, 173094540, 1632480259, 15851668551, 157824649955, 1605839173312, 16652321922596, 175596537163347, 1879357191026029, 20382942631855557, 223719376672365073, 2482094083780961295, 27808544385768051233

Offset: 0

N. J. A. Sloane, Mar 19 2015

nonn

Anthony Guttmann, Table of n, a(n) for n = 0..27
Nathan Clisby, Andrew R. Conway, Anthony J. Guttmann, Yuma Inoue, Classical length-5 pattern-avoiding permutations, arXiv:2109.13485 [math.CO], 2021.
Zvezdelina Stankova-Frenkel and Julian West, A new class of Wilf-equivalent permutations, arXiv:math/0103152 [math.CO], 2001.

Representatives for the 16 Wilf-equivalence patterns of length 5 are given in A116485, A047889, and A256195-A256208.

Cf. A099952.

avoid[n_, pat_] := Module[{p1 = pat[[1]], p2 = pat[[2]], p3 = pat[[3]], p4 = pat[[4]], p5 = pat[[5]], lseq = {}, i, p,
    lpat = Subsets[(n + 1) - Range[n], {Length[pat]}],
    psn = Permutations[Range[n]]},
   For[i = 1, i <= Length[lpat], i++,
    p = lpat[[i]];
    AppendTo[lseq, Select[psn, MemberQ[#, {_, p[[p1]], _, p[[p2]], _, p[[p3]], _, p[[p4]], _, p[[p5]], _}, {0}] &]];
    ]; n! - Length[Union[Flatten[lseq, 1]]]];
Table[avoid[n, {4, 3, 2, 5, 1}], {n, 0, 8}]  (* Robert Price, Mar 27 2020 *)

More terms from Anthony Guttmann, Sep 29 2021

A256204 Number of permutations in S_n that avoid the pattern 32541.

Original entry on oeis.org

1, 1, 2, 6, 24, 119, 694, 4581, 33284, 260847, 2172454, 19015582, 173461305, 1638327423, 15939733122, 159099927785, 1623799173782, 16900201391546, 178967276844263, 1924689980696921, 20987593594256974, 231734179050033660, 2587835777992844938, 29198736751160012102

Offset: 0

N. J. A. Sloane, Mar 19 2015

nonn

Anthony Guttmann, Table of n, a(n) for n = 0..26
Nathan Clisby, Andrew R. Conway, Anthony J. Guttmann, Yuma Inoue, Classical length-5 pattern-avoiding permutations, arXiv:2109.13485 [math.CO], 2021.
Zvezdelina Stankova-Frenkel and Julian West, A new class of Wilf-equivalent permutations, arXiv:math/0103152 [math.CO], 2001.

Representatives for the 16 Wilf-equivalence patterns of length 5 are given in A116485, A047889, and A256195-A256208.

Cf. A099952.

avoid[n_, pat_] := Module[{p1 = pat[[1]], p2 = pat[[2]], p3 = pat[[3]], p4 = pat[[4]], p5 = pat[[5]], lseq = {}, i, p,
    lpat = Subsets[(n + 1) - Range[n], {Length[pat]}],
    psn = Permutations[Range[n]]},
   For[i = 1, i <= Length[lpat], i++,
    p = lpat[[i]];
    AppendTo[lseq, Select[psn, MemberQ[#, {_, p[[p1]], _, p[[p2]], _, p[[p3]], _, p[[p4]], _, p[[p5]], _}, {0}] &]];
    ]; n! - Length[Union[Flatten[lseq, 1]]]];
Table[avoid[n, {3, 2, 5, 4, 1}], {n, 0, 8}]  (* Robert Price, Mar 27 2020 *)

More terms from Anthony Guttmann, Sep 29 2021

A256205 Number of permutations in S_n that avoid the pattern 34215.

Original entry on oeis.org

1, 1, 2, 6, 24, 119, 694, 4581, 33285, 260886, 2173374, 19032746, 173741467, 1642533692, 15999488304, 159917206735, 1634681988983, 17042352950764, 180798150762914, 1948027746498015, 21282786390947602, 235446451502773103, 2634317655935012208, 29778833170013213300

Offset: 0

N. J. A. Sloane, Mar 19 2015

nonn

Anthony Guttmann, Table of n, a(n) for n = 0..27
Nathan Clisby, Andrew R. Conway, Anthony J. Guttmann, Yuma Inoue, Classical length-5 pattern-avoiding permutations, arXiv:2109.13485 [math.CO], 2021.
Zvezdelina Stankova-Frenkel and Julian West, A new class of Wilf-equivalent permutations, arXiv:math/0103152 [math.CO], 2001.

Representatives for the 16 Wilf-equivalence patterns of length 5 are given in A116485, A047889, and A256195-A256208.

Cf. A099952.

avoid[n_, pat_] := Module[{p1 = pat[[1]], p2 = pat[[2]], p3 = pat[[3]], p4 = pat[[4]], p5 = pat[[5]], lseq = {}, i, p,
    lpat = Subsets[(n + 1) - Range[n], {Length[pat]}],
    psn = Permutations[Range[n]]},
   For[i = 1, i <= Length[lpat], i++,
    p = lpat[[i]];
    AppendTo[lseq, Select[psn, MemberQ[#, {_, p[[p1]], _, p[[p2]], _, p[[p3]], _, p[[p4]], _, p[[p5]], _}, {0}] &]];
    ]; n! - Length[Union[Flatten[lseq, 1]]]];
Table[avoid[n, {3, 4, 2, 1, 5}], {n, 0, 8}]  (* Robert Price, Mar 27 2020 *)

More terms from Anthony Guttmann, Sep 29 2021

A256206 Number of permutations in S_n that avoid the pattern 42315.

Original entry on oeis.org

1, 1, 2, 6, 24, 119, 694, 4581, 33287, 260967, 2175379, 19072271, 174426353, 1653484169, 16165513608, 162344264849, 1669261805697, 17526017429722, 187472773174466, 2039233971499931, 22520066337196663, 252141732452056894, 2858721279079666465, 32786666580814894741

Offset: 0

N. J. A. Sloane, Mar 19 2015

nonn

Anthony Guttmann, Table of n, a(n) for n = 0..26
Nathan Clisby, Andrew R. Conway, Anthony J. Guttmann, Yuma Inoue, Classical length-5 pattern-avoiding permutations, arXiv:2109.13485 [math.CO], 2021.
Zvezdelina Stankova-Frenkel and Julian West, A new class of Wilf-equivalent permutations, arXiv:math/0103152 [math.CO], 2001.

Representatives for the 16 Wilf-equivalence patterns of length 5 are given in A116485, A047889, and A256195-A256208.

Cf. A099952.

avoid[n_, pat_] := Module[{p1 = pat[[1]], p2 = pat[[2]], p3 = pat[[3]], p4 = pat[[4]], p5 = pat[[5]], lseq = {}, i, p,
    lpat = Subsets[(n + 1) - Range[n], {Length[pat]}],
    psn = Permutations[Range[n]]},
   For[i = 1, i <= Length[lpat], i++,
    p = lpat[[i]];
    AppendTo[lseq, Select[psn, MemberQ[#, {_, p[[p1]], _, p[[p2]], _, p[[p3]], _, p[[p4]], _, p[[p5]], _}, {0}] &]];
    ]; n! - Length[Union[Flatten[lseq, 1]]]];
Table[avoid[n, {4, 2, 3, 1, 5}], {n, 0, 8}]  (* Robert Price, Mar 27 2020 *)

More terms from Anthony Guttmann, Sep 29 2021

A256207 Number of permutations in S_n that avoid the pattern 53421.

Original entry on oeis.org

1, 1, 2, 6, 24, 119, 694, 4582, 33325, 261853, 2191902, 19344408, 178582940, 1713999264, 17019444969, 174149184184, 1830279810276, 19703572779755, 216769635980879, 2432308876304981, 27788506478197951, 322770995262901091, 3806657237502632706, 45532086120583546634

Offset: 0

N. J. A. Sloane, Mar 19 2015

nonn

Anthony Guttmann, Table of n, a(n) for n = 0..26
Nathan Clisby, Andrew R. Conway, Anthony J. Guttmann, Yuma Inoue, Classical length-5 pattern-avoiding permutations, arXiv:2109.13485 [math.CO], 2021.
Zvezdelina Stankova-Frenkel and Julian West, A new class of Wilf-equivalent permutations, arXiv:math/0103152 [math.CO], 2001.

Representatives for the 16 Wilf-equivalence patterns of length 5 are given in A116485, A047889, and A256195-A256208.

Cf. A099952.

avoid[n_, pat_] := Module[{p1 = pat[[1]], p2 = pat[[2]], p3 = pat[[3]], p4 = pat[[4]], p5 = pat[[5]], lseq = {}, i, p,
    lpat = Subsets[(n + 1) - Range[n], {Length[pat]}],
    psn = Permutations[Range[n]]},
   For[i = 1, i <= Length[lpat], i++,
    p = lpat[[i]];
    AppendTo[lseq, Select[psn, MemberQ[#, {_, p[[p1]], _, p[[p2]], _, p[[p3]], _, p[[p4]], _, p[[p5]], _}, {0}] &]];
    ]; n! - Length[Union[Flatten[lseq, 1]]]];
Table[avoid[n, {5, 3, 4, 2, 1}], {n, 0, 8}]  (* Robert Price, Mar 27 2020 *)

More terms from Anthony Guttmann, Sep 29 2021

cp's OEIS Frontend

A256202 Number of permutations in S_n that avoid the pattern 53241.

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A256203 Number of permutations in S_n that avoid the pattern 43251.

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Author

Keywords

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Programs

Mathematica

Extensions

A256204 Number of permutations in S_n that avoid the pattern 32541.

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Author

Keywords

Links

Crossrefs

Programs

Mathematica

Extensions

A256205 Number of permutations in S_n that avoid the pattern 34215.

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Author

Keywords

Links

Crossrefs

Programs

Mathematica

Extensions

A256206 Number of permutations in S_n that avoid the pattern 42315.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Extensions

A256207 Number of permutations in S_n that avoid the pattern 53421.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Extensions