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.

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A177526 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, down.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 680, 4480, 33600, 285434, 2684680, 27812170, 313926560, 3842611240, 50625902600, 714873188122, 10764733339179, 172258243070682, 2918333808555034, 52191694000877878, 982479378895814520, 19419959862935129834, 402131210857811703926
Offset: 0

Views

Author

R. H. Hardin, May 10 2010

Keywords

Links

Crossrefs

Columns k=18,22 of A242784.

Programs

  • Maple
    b:= proc(u, o, t) option remember; `if`(t>5, 0, `if`(u+o=0, 1,
      add(b(u-j, o+j-1, [1, 3, 4, 1, 6][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 2, 5, 2][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 21 2013
  • Mathematica
    b[u_, o_, t_] := b[u, o, t] = If[t > 5, 0, If[u + o + t < 6, (u + o)!,
     Sum[b[u - j, o + j - 1, {1, 3, 4, 1, 6}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 2, 5, 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 *)

Formula

a(n) ~ c * d^n * n!, where d = 0.94123983763344712685016041467..., c = 1.3558011859159420827133973526... . - Vaclav Kotesovec, Jan 17 2015

Extensions

a(17)-a(22) from Alois P. Heinz, Oct 21 2013

A177527 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, up.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 694, 4676, 35952, 310464, 2984176, 31536583, 363591384, 4541789148, 61089594448, 880428095803, 13534614549829, 221066397540186, 3823205871530350, 69792946997645295, 1341134146478847104, 27059669661295560098, 571973335506443017436
Offset: 0

Views

Author

R. H. Hardin, May 10 2010

Keywords

Links

Crossrefs

Columns k=19,25 of A242784.

Programs

  • Maple
    b:= proc(u, o, t) option remember; `if`(t>5, 0, `if`(u+o=0, 1,
      add(b(u-j, o+j-1, [1,3,4,1,3][t]), j=1..u)+
      add(b(u+j-1, o-j, [2,2,2,5,6][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 21 2013
  • Mathematica
    b[u_, o_, t_] := b[u, o, t] = If[t > 5, 0, If[u + o + t < 6, (u + o)!,
     Sum[b[u - j, o + j - 1, {1, 3, 4, 1, 3}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 2, 5, 6}[[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 *)

Formula

a(n) ~ c * d^n * n!, where d = 0.96079505301634594056671142147783512755736606..., c = 1.2266835832918378326758739778897107143678546... . - Vaclav Kotesovec, Jan 17 2015

Extensions

a(17)-a(22) from Alois P. Heinz, Oct 21 2013

A177529 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, down, up.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 659, 4186, 31457, 264834, 2465550, 25334981, 283322383, 3430384284, 44803783445, 626719448981, 9347396890481, 148174002240074, 2486833885400060, 44052337160572208, 821495697573151302, 16085109561896603059, 329939476998354570978
Offset: 0

Views

Author

R. H. Hardin, May 10 2010

Keywords

Links

Crossrefs

Column k=21 of A242784.

Programs

  • Maple
    b:= proc(u, o, t) option remember; `if`(t>5, 0, `if`(u+o+t<6, (u+o)!,
      add(b(u-j, o+j-1, [1, 3, 1, 5, 1][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 4, 2, 6][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 21 2013
  • Mathematica
    b[u_, o_, t_] := b[u, o, t] = If[t > 5, 0, If[u + o + t < 6, (u + o)!,
     Sum[b[u - j, o + j - 1, {1, 3, 1, 5, 1}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 4, 2, 6}[[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 *)

Formula

a(n) ~ c * d^n * n!, where d = 0.9323832531422843725281328190771918152..., c = 1.369593476632786981162993013559816... . - Vaclav Kotesovec, Jan 17 2015

A177530 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, up, up.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 706, 4844, 37968, 334656, 3278896, 35330098, 415289184, 5288377848, 72522052240, 1065579141202, 16700472769061, 278099720959114, 4903387952699182, 91258390273541562, 1787828412527348984, 36776310494510881628, 792526608079806841508
Offset: 0

Views

Author

R. H. Hardin, May 10 2010

Keywords

Links

Crossrefs

Columns k=23,29 of A242784.

Programs

  • Maple
    b:= proc(u, o, t) option remember; `if`(t>5, 0, `if`(u+o+t<6, (u+o)!,
      add(b(u-j, o+j-1, [1, 3, 1, 3, 3][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 4, 5, 6][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 21 2013
  • Mathematica
    b[u_, o_, t_] := b[u, o, t] = If[t > 5, 0, If[u + o + t < 6, (u + o)!,
     Sum[b[u - j, o + j - 1, {1, 3, 1, 3, 3}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 4, 5, 6}[[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 *)

Formula

a(n) ~ c * d^n * n!, where d = 0.9795419074893388679910049642242424087370823270695747551625158..., c = 1.111068410182136129001099552719852410280865324840041630689... . - Vaclav Kotesovec, Jan 17 2015

Extensions

a(17)-a(22) from Alois P. Heinz, Oct 21 2013

A177531 Number of permutations of {1,...,n} avoiding adjacent step pattern up, up, down, down, down.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 710, 4900, 38640, 342720, 3376800, 36603975, 432850200, 5545086300, 76500496800, 1130799033000, 17829310686875, 298684478837750, 5298029559119250, 99196696006173000, 1955043380032965000, 40458045505003152500, 877115498011253207500
Offset: 0

Views

Author

R. H. Hardin, May 10 2010

Keywords

Links

Crossrefs

Columns k=24,28 of A242784.

Programs

  • Maple
    b:= proc(u, o, t) option remember; `if`(t>5, 0, `if`(u+o+t<6, (u+o)!,
      add(b(u-j, o+j-1, [1, 1, 4, 5, 6][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 3, 3, 2, 2][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 21 2013
  • Mathematica
    b[u_, o_, t_] := b[u, o, t] = If[t > 5, 0, If[u + o + t < 6, (u + o)!,
     Sum[b[u - j, o + j - 1, {1, 1, 4, 5, 6}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 3, 3, 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 *)

Formula

a(n) ~ c * d^n * n!, where d = 0.9854377717049233842779147747459503689075051143455990422632259770134..., c = 1.077575450109847511736343360036618345267367515043056772740942767... . - Vaclav Kotesovec, Jan 17 2015

Extensions

a(17)-a(22) from Alois P. Heinz, Oct 21 2013

A177532 Number of permutations of {1,...,n} avoiding adjacent step pattern up, up, down, up, up.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 701, 4774, 37128, 326089, 3184221, 34191983, 400308461, 5076257396, 69329710171, 1014612340743, 15838898430094, 262706269352374, 4613506518038420, 85520547931176984, 1668736482655334275, 34189755475407632542, 733851215342599413848
Offset: 0

Views

Author

R. H. Hardin, May 10 2010

Keywords

Links

Crossrefs

Column k=27 of A242784.

Programs

  • Maple
    b:= proc(u, o, t) option remember; `if`(t>5, 0, `if`(u+o+t<6, (u+o)!,
      add(b(u-j, o+j-1, [1, 1, 4, 1, 1][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 3, 3, 5, 6][t]), j=1..o)))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 21 2013
  • Mathematica
    b[u_, o_, t_] := b[u, o, t] = If[t > 5, 0, If[u + o + t < 6, (u + o)!,
     Sum[b[u - j, o + j - 1, {1, 1, 4, 1, 1}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 3, 3, 5, 6}[[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 *)

Formula

a(n) ~ c * d^n * n!, where d = 0.975638124670183802889377522566191208591041394..., c = 1.123281860028517266849117754708517961017398615... . - Vaclav Kotesovec, Jan 17 2015

Extensions

a(17)-a(22) from Alois P. Heinz, Oct 21 2013

A177534 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, down, down, down.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 720, 5034, 40224, 361584, 3611520, 39679200, 475580160, 6175139244, 86348433264, 1293675609960, 20674025187840, 351037594569600, 6311110770685440, 119767524064039062, 2392482308124881520, 50181968955048369480, 1102681392427432825920
Offset: 0

Views

Author

R. H. Hardin, May 10 2010

Keywords

Links

Crossrefs

Columns k=32,62 of A242784.

Programs

  • Maple
    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, `if`(t=1, 1, t+1)), j=1..u)+
      add(b(u+j-1, o-j, 2), j=1..o)))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 21 2013
  • Mathematica
    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, If[t == 1, 1, t + 1]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, 2], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 20 2022, after Alois P. Heinz *)

Formula

a(n) ~ c * d^n * n!, where d = 0.99880260814201465936657157017137377717606254472452619578417647021809..., c = 1.0072348951217738673562195411256011395302888145883911883919110478... . - Vaclav Kotesovec, Jan 17 2015

Extensions

a(18)-a(22) from Alois P. Heinz, Oct 21 2013

A177535 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, down, down, up.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 720, 5011, 39856, 356616, 3545280, 38768400, 462487631, 5977005477, 83186290826, 1240460869290, 19730730733920, 333451122953921, 5966845400766578, 112703780178989573, 2240828272067529040, 46780834679854338540, 1023129822229674425971
Offset: 0

Views

Author

R. H. Hardin, May 10 2010

Keywords

Links

Crossrefs

Column k=33 of A242784.

Programs

  • Maple
    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, 5, 6, 1][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 2, 2, 2, 7][t]), j=1..o)))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 22 2013
  • Mathematica
    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, 5, 6, 1}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 2, 2, 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 *)

Formula

a(n) ~ c * d^n * n!, where d = 0.9941229421721758523485136789468386588070503717223814960732680334748287519..., c = 1.036291721564809563490641628457988175489113294377683691938047314400726... . - Vaclav Kotesovec, Jan 17 2015

Extensions

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

A177536 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, down, up, down.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 720, 4962, 39072, 346032, 3404160, 36853442, 435133488, 5566069380, 76676528112, 1131700250442, 17817052536384, 298034349244128, 5278625637077376, 98686282426953080, 1942087278998014400, 40130098178033129036, 868710371909527352944
Offset: 0

Views

Author

R. H. Hardin, May 10 2010

Keywords

Links

Crossrefs

Column k=34,46 of A242784.

Programs

  • Maple
    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, 5, 1, 7][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 2, 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
  • Mathematica
    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, 5, 1, 7}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 2, 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 *)

Formula

a(n) ~ c * d^n * n!, where d = 0.983970585738736307495769238852152954976022611246..., c = 1.1028129540167952253429967393297373345979852081... . - Vaclav Kotesovec, Jan 17 2015

Extensions

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

A177537 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, down, up, up.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 720, 4985, 39440, 351000, 3470400, 37738800, 447766925, 5755249449, 79663786022, 1181466923370, 18690124534560, 314145239141775, 5590784473674106, 105025821614503735, 2076805450110696320, 43120601826854807940, 937944680532722764045
Offset: 0

Views

Author

R. H. Hardin, May 10 2010

Keywords

Links

Crossrefs

Columns k=35,49 of A242784.

Programs

  • Maple
    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, 5, 1, 3][t]), j=1..u)+
      add(b(u+j-1, o-j, [2, 2, 2, 2, 6, 7][t]), j=1..o)))
    end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);  # Alois P. Heinz, Oct 24 2013
  • Mathematica
    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, 5, 1, 3}[[t]]], {j, 1, u}] +
     Sum[b[u + j - 1, o - j, {2, 2, 2, 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 *)

Formula

a(n) ~ c * d^n * n!, where d = 0.9887118103491926984294539697508784179435508781692068887..., c = 1.071215254418408841713627749833237640463228021776737... . - Vaclav Kotesovec, Jan 17 2015

Extensions

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