cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 21-29 of 29 results.

A256201 Number of permutations in S_n that avoid the pattern 35241.

Original entry on oeis.org

1, 1, 2, 6, 24, 119, 694, 4580, 33254, 260285, 2163930, 18900534, 172016256, 1621031261, 15739870457, 156855197297, 1599233708733, 16638560125635, 176269571712376, 1898076560618372, 20742488003444465, 229747253093647567, 2576270755655436479, 29218474225923168362
Offset: 0

Views

Author

N. J. A. Sloane, Mar 19 2015

Keywords

Links

Crossrefs

Representatives for the 16 Wilf-equivalence patterns of length 5 are given in A116485, A047889, and A256195-A256208.
Cf. A099952.

Programs

  • Mathematica
    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, 5, 2, 4, 1}], {n, 0, 8}]  (* Robert Price, Mar 27 2020 *)

Extensions

More terms from Anthony Guttmann, Sep 29 2021

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

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Mar 19 2015

Keywords

Links

Crossrefs

Representatives for the 16 Wilf-equivalence patterns of length 5 are given in A116485, A047889, and A256195-A256208.
Cf. A099952.

Programs

  • Mathematica
    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 *)

Extensions

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

Views

Author

N. J. A. Sloane, Mar 19 2015

Keywords

Links

Crossrefs

Representatives for the 16 Wilf-equivalence patterns of length 5 are given in A116485, A047889, and A256195-A256208.
Cf. A099952.

Programs

  • Mathematica
    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 *)

Extensions

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

Views

Author

N. J. A. Sloane, Mar 19 2015

Keywords

Links

Crossrefs

Representatives for the 16 Wilf-equivalence patterns of length 5 are given in A116485, A047889, and A256195-A256208.
Cf. A099952.

Programs

  • Mathematica
    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 *)

Extensions

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

Views

Author

N. J. A. Sloane, Mar 19 2015

Keywords

Links

Crossrefs

Representatives for the 16 Wilf-equivalence patterns of length 5 are given in A116485, A047889, and A256195-A256208.
Cf. A099952.

Programs

  • Mathematica
    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 *)

Extensions

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

Views

Author

N. J. A. Sloane, Mar 19 2015

Keywords

Links

Crossrefs

Representatives for the 16 Wilf-equivalence patterns of length 5 are given in A116485, A047889, and A256195-A256208.
Cf. A099952.

Programs

  • Mathematica
    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 *)

Extensions

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

Views

Author

N. J. A. Sloane, Mar 19 2015

Keywords

Links

Crossrefs

Representatives for the 16 Wilf-equivalence patterns of length 5 are given in A116485, A047889, and A256195-A256208.
Cf. A099952.

Programs

  • Mathematica
    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 *)

Extensions

More terms from Anthony Guttmann, Sep 29 2021

A224180 Number of permutations of length n containing exactly 1 occurrence of 12354.

Original entry on oeis.org

0, 0, 0, 0, 1, 19, 246, 2767, 29384, 305646, 3170684, 33104118, 349462727, 3738073247, 40549242195, 446115153023, 4976319258200, 56252653681606, 643996994735079, 7461850038335967, 87447167319345337, 1035866799853591309, 12395264890256322913
Offset: 1

Views

Author

Brian Nakamura, Apr 01 2013

Keywords

Links

Crossrefs

Cf. A047889.

Programs

  • Maple
    Programs can be obtained from the link.

A224250 Number of permutations in S_n containing exactly 2 increasing subsequences of length 5.

Original entry on oeis.org

0, 0, 0, 0, 0, 5, 128, 2124, 29445, 373379, 4517921, 53342405, 622358262, 7229196009, 83984283157, 978558652802, 11455522117193, 134879815196252, 1598299236441571, 19067702481168369
Offset: 1

Views

Author

Brian Nakamura, Apr 02 2013

Keywords

References

  • B. Nakamura and D. Zeilberger, Using Noonan-Zeilberger Functional Equations to enumerate (in Polynomial Time!) Generalized Wilf classes, Adv. in Appl. Math. 50 (2013), 356-366.

Links

Crossrefs

Cf. A047889, A224248.

Programs

  • Maple
    # programs can be obtained from the Nakamura and Zeilberger link.
Previous Showing 21-29 of 29 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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