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.

Showing 1-7 of 7 results.

A376694 Number of permutations of order n avoiding consecutive pattern 121'3.

Original entry on oeis.org

1, 1, 2, 6, 22, 100, 548, 3482, 25256, 206298, 1871704, 18676354, 203323724, 2397969518, 30455963576, 414446765490, 6015821216380, 92778775395190, 1515047281161392, 26114701159308242, 473827422862284740, 9027024454944900390, 180165845677134636856, 3759286756628732868754, 81850596163629861103004
Offset: 0

Views

Author

Max Alekseyev, Oct 01 2024

Keywords

Comments

To avoid 121'3 means not to have four consecutive letters such that the first letter and the third one is less than the second, and the second one is less than and the fourth one.

Links

Crossrefs

Cf. A117156, A177470, A177471, A177472, A177473, A177475, A177476, A177477, A177478, A177479, A177480, A177481, A177482, A177483, A177484.

A177472 Number of permutations of order n avoiding the consecutive pattern 11'2'2.

Original entry on oeis.org

1, 1, 2, 6, 18, 71, 322, 1665, 9789, 64327, 468914, 3748920, 32699022, 308710917, 3138821688, 34186918427, 397173376849, 4902547569617, 64073734206528, 883940288032392, 12836250526983672, 195724485831901029, 3126468139092090818, 52211816154041174670, 909843384081141844312
Offset: 0

Views

Author

Signy Olafsdottir (signy06(AT)ru.is), May 09 2010

Keywords

Comments

To avoid 11'2'2 means not to have four consecutive letters such that the first letter is less than the last one, and the second letter is less than the third one.

Links

Crossrefs

Cf. A117156, A177470, A177471, A177473, A177475, A177476, A177477, A177478, A177479, A177480, A177481, A177482, A177483, A177484, A376694.

Extensions

Edited and terms a(0), a(10)-a(24) added by Max Alekseyev, Oct 02 2024

A177473 Number of permutations of order n avoiding the consecutive pattern 12'1'2.

Original entry on oeis.org

1, 1, 2, 6, 18, 61, 272, 1410, 8048, 51550, 372995, 2976679, 25686748, 239687103, 2419267562, 26194183096, 301838412516, 3692782460824, 47891164866100, 655887513203263, 9449915113835659, 142923476094740969, 2265214890150056647, 37539217881003574022, 649054317768293760078
Offset: 0

Views

Author

Signy Olafsdottir (signy06(AT)ru.is), May 09 2010

Keywords

Comments

To avoid 12'1'2 means not to have four consecutive letters such that the first one is less than the fourth letter and the second letter is larger than the third one.

Links

Crossrefs

Cf. A117156, A177470, A177471, A177472, A177475, A177476, A177477, A177478, A177479, A177480, A177481, A177482, A177483, A177484, A376694.

Extensions

Edited and terms a(0), a(10)-a(24) added by Max Alekseyev, Oct 01 2024

A177475 Number of permutations of order n avoiding the consecutive pattern 131'2.

Original entry on oeis.org

1, 1, 2, 6, 20, 81, 390, 2161, 13678, 96983, 764368, 6630898, 62748250, 643442919, 7104914398, 84062375725, 1060919238874, 14226075039395, 201982580807466, 3027049675655253, 47753241018325280, 790998083929598213, 13726222157931958274, 249018700470309832015, 4714071198944211367704
Offset: 0

Views

Author

Signy Olafsdottir (signy06(AT)ru.is), May 09 2010

Keywords

Comments

To avoid 131'2 means not to have four consecutive letters such that if the third letter is removed, then in the obtained 3 letter word the smallest letter is the first one, and the largest letter is the second one.

Links

Crossrefs

Cf. A117156, A177470, A177471, A177472, A177473, A177476, A177477, A177478, A177479, A177480, A177481, A177482, A177483, A177484, A376694.

Extensions

Edited and terms a(0),a(10)-a(24) added by Max Alekseyev, Oct 02 2024

A177476 Number of partitions of order n avoiding the consecutive pattern 231'1.

Original entry on oeis.org

1, 1, 2, 6, 20, 83, 402, 2245, 14192, 100650, 792508, 6859260, 64772648, 662630653, 7301841444, 86212535179, 1085834949064, 14530898302390, 205897508769218, 3079580500287978, 48485072137150344, 801518797091165406, 13881049047327393608, 251325130816997882224, 4748240560493406374592
Offset: 0

Views

Author

Signy Olafsdottir (signy06(AT)ru.is), May 09 2010

Keywords

Comments

To avoid 231'1 means not to have four consecutive letters such that if the third letter is removed, then in the obtained 3 letter word the smallest letter is the last one, and the largest letter is the second one.

Links

Crossrefs

Cf. A117156, A177470, A177471, A177472, A177473, A177475, A177477, A177478, A177479, A177480, A177481, A177482, A177483, A177484, A376694.

Programs

  • Mathematica
    ok[{x_, y_, , z}] := Not[x>z && y>z && y>x]; a[n_] := Length@ Select[ Permutations@ Range@ n, AllTrue[ Partition[#, 4, 1], ok] &]; a /@ Range[0, 9]

Extensions

a(0), a(10)-a(14) from Alois P. Heinz, Mar 10 2020
a(15)-a(16) from Giovanni Resta, Mar 11 2020
a(17)-a(24) from Max Alekseyev, Oct 02 2024

A177480 Number of permutations of order n avoiding the consecutive pattern egfh with e

Original entry on oeis.org

1, 1, 2, 6, 20, 84, 412, 2300, 14676, 104536, 825660, 7168860, 67826340, 695174208, 7671602644, 90700227700, 1143825611348, 15325929083336, 217429459642252, 3256039887793868, 51325896829151684, 849518895902379696, 14730333827970237220, 267028337196612514596, 5051094767395355339476
Offset: 0

Views

Author

Signy Olafsdottir (signy06(AT)ru.is), May 09 2010

Keywords

Comments

To avoid egfh means not to have four consecutive letters such that the first and the second letters are less than the third and the fourth letters.

Links

Crossrefs

Cf. A117156, A177470, A177471, A177472, A177473, A177475, A177476, A177477, A177478, A177479, A177481, A177482, A177483, A177484, A376694.

Programs

  • Mathematica
    ok[{e_, f_, g_, h_}] := e > g || e > h || f > g || f > h; a[n_] := Length@ Select[ Permutations[Range@n], AllTrue[ Partition[#, 4, 1], ok] &]; a /@ Range[0, 9] (* Giovanni Resta, Mar 11 2020 *)

Extensions

a(0), a(10)-a(14) from Alois P. Heinz, Mar 10 2020
a(15)-a(16) from Giovanni Resta, Mar 11 2020
Edited and a(17)-a(24) added by Max Alekseyev, Oct 01 2024

A177481 Number of permutations of order n avoiding the consecutive pattern efgh with e

Original entry on oeis.org

1, 1, 2, 6, 20, 80, 404, 2368, 15488, 114480, 948992, 8625672, 85223792, 913869056, 10567326528, 130796711016, 1726077013456, 24213357455936, 359694651093152, 5638959807231240, 93052021458248400, 1612444736747193696, 29271726199933801536, 555518182602741687432, 11001032351303890637648
Offset: 0

Views

Author

Signy Olafsdottir (signy06(AT)ru.is), May 09 2010

Keywords

Comments

To avoid efgh means not to have four consecutive letters such that the first and the third letters are less than the second and the fourth letters.

Links

Crossrefs

Cf. A117156, A177470, A177471, A177472, A177473, A177475, A177476, A177477, A177478, A177479, A177480, A177482, A177483, A177484, A376694.

Programs

  • Mathematica
    ok[{e_,f_,g_,h_}] := e>f || e>h || g>f || g>h; a[n_] := Length@ Select[ Permutations[ Range@ n], AllTrue[ Partition[#, 4, 1], ok] &]; Array[a, 9, 0] (* Giovanni Resta, Mar 11 2020 *)

Extensions

a(0), a(10)-a(16) from Giovanni Resta, Mar 11 2020
Edited and a(17)-a(24) added by Max Alekseyev, Oct 01 2024
Showing 1-7 of 7 results.

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