A242784 -id:A242784 - cp's OEIS frontend

A177538 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, down, down.

1, 1, 2, 6, 24, 120, 720, 4941, 38736, 341496, 3354939, 36244098, 427006404, 5448087216, 74864913552, 1102353646680, 17314190063037, 288936154260522, 5105249306345502, 95216905474054011, 1869347069817467076, 38535066745735462848, 832195054189721911392

Offset: 0

R. H. Hardin, May 10 2010

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..200

Columns k=36,54 of A242784.

b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,
      add(b(u-j, o+j-1, [1, 3, 4, 1, 6, 7][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 2, 5, 2, 2][t]), j=1..o)))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 22 2013

b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
     Sum[b[u - j, o + j - 1, {1, 3, 4, 1, 6, 7}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 2, 5, 2, 2}[[t]]], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 19 2022, after Alois P. Heinz *)

a(n) ~ c * d^n * n!, where d = 0.98162590771907099517875504406285427992737137228..., c = 1.1133866874983726502599853171771818959460675... . - Vaclav Kotesovec, Jan 17 2015

a(17)-a(22) from Alois P. Heinz, Oct 22 2013

A177539 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, down, up.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 720, 4859, 37424, 323784, 3107520, 32749200, 376929246, 4698101279, 63058148792, 906829731450, 13911580276800, 226738605155619, 3912973221007668, 71280397766349665, 1366816300552776920, 27519285653572655340, 580456044040809459821

Offset: 0

R. H. Hardin, May 10 2010

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..175

Columns k=37,41 of A242784.

b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,
      add(b(u-j, o+j-1, [1, 3, 4, 1, 6, 4][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 2, 5, 2, 7][t]), j=1..o)))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 24 2013

b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
     Sum[b[u - j, o + j - 1, {1, 3, 4, 1, 6, 4}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 2, 5, 2, 7}[[t]]], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 19 2022, after Alois P. Heinz *)

a(n) ~ c * d^n * n!, where d = 0.958757960478580745672487123002941621817..., c = 1.30438280919882137519668832091857761... . - Vaclav Kotesovec, Jan 17 2015

a(17)-a(22) from Alois P. Heinz, Oct 24 2013

A177540 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, up, down.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 720, 4908, 38208, 334368, 3248640, 34774112, 405758208, 5129918808, 69849531936, 1018876044528, 15854497560576, 262116761475488, 4588408779868800, 84784281517177940, 1649073291620014880, 33678805727832427224, 720569710852319474016

Offset: 0

R. H. Hardin, May 10 2010

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..175

Column k=38 of A242784.

b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,
      add(b(u-j, o+j-1, [1, 3, 4, 1, 3, 7][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 2, 5, 6, 2][t]), j=1..o)))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 24 2013

b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
     Sum[b[u - j, o + j - 1, {1, 3, 4, 1, 3, 7}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 2, 5, 6, 2}[[t]]], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 19 2022, after Alois P. Heinz *)

a(n) ~ c * d^n * n!, where d = 0.97251576612005359341988641793523250275..., c = 1.18354011206219905745522624899424386... . - Vaclav Kotesovec, Jan 17 2015

a(17)-a(22) from Alois P. Heinz, Oct 24 2013

A177541 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, up, up.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 720, 4990, 39520, 352080, 3484800, 37936800, 450606300, 5797965980, 80341280840, 1192794269400, 18889568419200, 317838157969125, 5662578565559400, 106488682710940108, 2107992477960872320, 43815112964794432080, 954074378001971825930

Offset: 0

R. H. Hardin, May 10 2010

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..150

Columns k=39,57 of A242784.

b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o=0, 1,
      add(b(u-j, o+j-1, [1, 3, 4, 1, 3, 3][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 2, 5, 6, 7][t]), j=1..o)))
    end:
a:= n-> `if`(n=0, 1, add(b(j-1, n-j, 1), j=1..n)):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 20 2013

b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
     Sum[b[u - j, o + j - 1, {1, 3, 4, 1, 3, 3}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 2, 5, 6, 7}[[t]]], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 19 2022, after Alois P. Heinz *)

a(n) ~ c * d^n * n!, where d = 0.98977300089321592191180343193285102663621683..., c = 1.06422234334396404091033045795479059186356... . - Vaclav Kotesovec, Jan 17 2015

a(17)-a(22) from Alois P. Heinz, Oct 20 2013

A177542 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, down, down, down.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 720, 4976, 39296, 349056, 3444480, 37382400, 442506240, 5674931536, 78376004800, 1159755383520, 18305304913920, 306984257241600, 5451042337781760, 102170107109747648, 2015786374006453760, 41759419845040968960, 906291283573022730240

Offset: 0

R. H. Hardin, May 10 2010

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..175

Columns k=40,58 of A242784.

b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,
      add(b(u-j, o+j-1, [1, 3, 1, 5, 6, 7][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 4, 2, 4, 2][t]), j=1..o)))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 24 2013

b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
     Sum[b[u - j, o + j - 1, {1, 3, 1, 5, 6, 7}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 4, 2, 4, 2}[[t]]], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 19 2022, after Alois P. Heinz *)

a(n) ~ c * d^n * n!, where d = 0.9864854125625269564394281614736489845203102136102401801..., c = 1.08769348749685060865572679319744616257509477068722272... . - Vaclav Kotesovec, Jan 17 2015

a(17)-a(22) from Alois P. Heinz, Oct 24 2013

A177543 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, down, up, down.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 720, 4768, 35968, 312064, 3004160, 31764480, 365798400, 4555499520, 61232590848, 882227765248, 13547017240576, 221038858829824, 3818608204709888, 69637156745773056, 1336921845773107200, 26947721453843251200, 569023211226594803712

Offset: 0

R. H. Hardin, May 10 2010

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..175

Column k=42 of A242784.

b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,
      add(b(u-j, o+j-1, [1, 3, 1, 5, 1, 7][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 4, 2, 6, 2][t]), j=1..o)))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 24 2013

b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
     Sum[b[u - j, o + j - 1, {1, 3, 1, 5, 1, 7}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 4, 2, 6, 2}[[t]]], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 19 2022, after Alois P. Heinz *)

a(n) ~ c * d^n * n!, where d = 0.9598365530271216889440240044515..., c = 1.2474579024498809739499621681... . - Vaclav Kotesovec, Jan 17 2015

a(17)-a(22) from Alois P. Heinz, Oct 24 2013

A177544 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, down, up, up.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 720, 4885, 37840, 329400, 3182400, 33778800, 391590750, 4915323791, 66442003448, 962278914330, 14866633343040, 244014015391725, 4240899164064012, 77799960323395327, 1502369690026049320, 30462229695574890900, 647071778569768101485

Offset: 0

R. H. Hardin, May 10 2010

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..200

Columns k=43,53 of A242784.

b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,
      add(b(u-j, o+j-1, [1, 3, 1, 5, 1, 5][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 4, 2, 6, 7][t]), j=1..o)))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 30 2013

b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
     Sum[b[u - j, o + j - 1, {1, 3, 1, 5, 1, 5}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 4, 2, 6, 7}[[t]]], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 19 2022, after Alois P. Heinz *)

a(n) ~ c * d^n * n!, where d = 0.96553264441829855042601163560012935129948..., c = 1.245410138868090155003662557978590938375... . - Vaclav Kotesovec, Jan 17 2015

a(17)-a(22) from Alois P. Heinz, Oct 30 2013

A177545 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, up, down, down.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 720, 4929, 38544, 338904, 3309120, 35521200, 415704960, 5271197205, 71977504692, 1053008012790, 16431803844480, 272435676775200, 4782657847248000, 88624515772410633, 1728678866577622920, 35404942557640528620, 759655818204633900000

Offset: 0

R. H. Hardin, May 10 2010

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..190

Columns k=44,50 of A242784.

b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,
      add(b(u-j, o+j-1, [1, 3, 1, 3, 6, 7][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 4, 5, 2, 4][t]), j=1..o)))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 22 2013

b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
     Sum[b[u - j, o + j - 1, {1, 3, 1, 3, 6, 7}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 4, 5, 2, 4}[[t]]], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 19 2022, after Alois P. Heinz *)

a(n) ~ c * d^n * n!, where d = 0.9752820884477652193970997660966130503977714987577677..., c = 1.1721546677937404500752065441275892023818795500231... . - Vaclav Kotesovec, Jan 17 2015

a(17)-a(22) from Alois P. Heinz, Oct 22 2013

A177546 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, up, down, up.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 720, 4871, 37616, 326376, 3161321, 33647702, 391315387, 4925158550, 66783060318, 969759198692, 15025115932355, 247300462549813, 4310409307848931, 79296721491391389, 1535659536831254219, 31225145160777718876, 665165555262983848987

Offset: 0

R. H. Hardin, May 10 2010

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..175

Column k=45 of A242784.

b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,
      add(b(u-j, o+j-1, [1, 3, 1, 3, 6, 1][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 4, 5, 2, 7][t]), j=1..o)))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 23 2013

b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
     Sum[b[u - j, o + j - 1, {1, 3, 1, 3, 6, 1}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 4, 5, 2, 7}[[t]]], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 19 2022, after Alois P. Heinz *)

a(n) ~ c * d^n * n!, where d = 0.968272411334148488816007705..., c = 1.2028586385369344074836174... . - Vaclav Kotesovec, Jan 17 2015

a(17)-a(22) from Alois P. Heinz, Oct 23 2013

A177547 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, up, up, up.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 720, 5020, 40000, 358560, 3571200, 39124800, 467612575, 6054492822, 84421683166, 1261227594360, 20098408531680, 340297488208325, 6100696794591542, 115446620042888642, 2299637587367422120, 48097983978364729800, 1053895947990450296810

Offset: 0

R. H. Hardin, May 10 2010

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..175

Columns k=47,61 of A242784.

b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,
      add(b(u-j, o+j-1, [1, 3, 1, 3, 3, 3][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 4, 5, 6, 7][t]), j=1..o)))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 23 2013

b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
     Sum[b[u - j, o + j - 1, {1, 3, 1, 3, 3, 3}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 4, 5, 6, 7}[[t]]], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 19 2022, after Alois P. Heinz *)

a(n) ~ c * d^n * n!, where d = 0.995974410535227680608696027123957375635061175769113923461462667..., c = 1.0246396933863574062731686342310661124393526441879248790690509... . - Vaclav Kotesovec, Jan 17 2015

a(17)-a(22) from Alois P. Heinz, Oct 23 2013

cp's OEIS Frontend

A177538 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, down, down.

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A177539 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, down, up.

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A177540 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, up, down.

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A177541 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, up, up.

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A177542 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, down, down, down.

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A177543 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, down, up, down.

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A177544 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, down, up, up.

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A177545 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, up, down, down.

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