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 11-20 of 25 results. Next

A152498 1/3 of the number of permutations of 2 indistinguishable copies of 1..n with exactly 6 local maxima.

Original entry on oeis.org

0, 0, 0, 0, 0, 76739, 42734373, 10478384089, 1717626773713, 222419564005134, 24781841211038024, 2496351029911357950, 234485896532293552830, 20959967704130971672341, 1807748255927878129526087, 151901517836714997413430591, 12521620421275657891377640951
Offset: 1

Views

Author

R. H. Hardin, Dec 06 2008

Keywords

Crossrefs

Cf. A334774.

Programs

  • PARI
    \\ PeaksBySig defined in A334774.
    a(n)={PeaksBySig(vector(n,i,2), [5])[1]/3}

Formula

a(n) = A334774(n,5)/3. - Andrew Howroyd, May 12 2020

Extensions

Terms a(11) and beyond from Andrew Howroyd, May 12 2020

A152500 1/4 the number of permutations of 3 indistinguishable copies of 1..n with exactly 3 local maxima.

Original entry on oeis.org

0, 1, 231, 21490, 1476084, 90050080, 5228286336, 297239712256, 16749407726592, 940343619493888, 52712719000338432, 2953100593082269696, 165399775808105742336, 9262957817232621568000, 518737995604927325405184, 29049593918675470746910720, 1626782962901824260072800256
Offset: 1

Views

Author

R. H. Hardin, Dec 06 2008

Keywords

Crossrefs

Programs

  • PARI
    \\ PeaksBySig defined in A334774.
    a(n) = {PeaksBySig(vector(n,i,3), [2])[1]/4} \\ Andrew Howroyd, May 12 2020
    
  • PARI
    concat(0, Vec(x^2*(1 + 123*x + 382*x^2 - 16548*x^3 - 15440*x^4) / ((1 - 4*x)^3*(1 - 20*x)^2*(1 - 56*x)) + O(x^19))) \\ Colin Barker, Jul 19 2020

Formula

From Colin Barker, Jul 19 2020: (Start)
G.f.: x^2*(1 + 123*x + 382*x^2 - 16548*x^3 - 15440*x^4) / ((1 - 4*x)^3*(1 - 20*x)^2*(1 - 56*x)).
a(n) = 108*a(n-1) - 3840*a(n-2) + 58752*a(n-3) - 401664*a(n-4) + 1244160*a(n-5) - 1433600*a(n-6) for n>6.
(End)

Extensions

Terms a(10) and beyond from Andrew Howroyd, May 12 2020

A152501 1/8 the number of permutations of 3 indistinguishable copies of 1..n with exactly 4 local maxima.

Original entry on oeis.org

0, 0, 46, 22615, 5036741, 819235874, 114962084772, 14974498962192, 1876234090571968, 230313563301166336, 27966954502164518912, 3376705184454377873408, 406486565581361073979392, 48857132166440216820449280, 5867654791849010140880306176, 704409107074292841154786361344
Offset: 1

Views

Author

R. H. Hardin, Dec 06 2008

Keywords

Crossrefs

Programs

  • PARI
    \\ PeaksBySig defined in A334774.
    a(n) = {PeaksBySig(vector(n,i,3), [3])[1]/8} \\ Andrew Howroyd, May 12 2020

Extensions

Terms a(9) and beyond from Andrew Howroyd, May 12 2020

A152502 1/12 of the number of permutations of 3 indistinguishable copies of 1..n with exactly 5 local maxima.

Original entry on oeis.org

0, 0, 1, 7274, 6251162, 2764274116, 897380159188, 247392790837624, 62200280199674352, 14820288466400312448, 3420153590479988396800, 774303834249035054901248, 173288568985609322651099136, 38513999874946087671220207616, 8524401267844398602674455314432
Offset: 1

Views

Author

R. H. Hardin, Dec 06 2008

Keywords

Crossrefs

Programs

  • PARI
    \\ PeaksBySig defined in A334774.
    a(n) = {PeaksBySig(vector(n,i,3), [4])[1]/12} \\ Andrew Howroyd, May 12 2020

Extensions

Terms a(9) and beyond from Andrew Howroyd, May 12 2020

A152503 1/8 of the number of permutations of 3 indistinguishable copies of 1..n with exactly 6 local maxima.

Original entry on oeis.org

0, 0, 0, 925, 5134608, 7080780596, 5503883684118, 3175651343215500, 1543855504958661492, 676391857775294288488, 277604477433374392213008, 109265969423431070616562496, 41856404659462959845867172864, 15752452465692536904424614273024, 5860017184412283112523269770190848
Offset: 1

Views

Author

R. H. Hardin, Dec 06 2008

Keywords

Crossrefs

Programs

  • PARI
    \\ PeaksBySig defined in A334774.
    a(n) = {PeaksBySig(vector(n,i,3), [5])[1]/8} \\ Andrew Howroyd, May 12 2020

Extensions

Terms a(9) and beyond from Andrew Howroyd, May 12 2020

A152505 1/10 of the number of permutations of 4 indistinguishable copies of 1..n with exactly 3 local maxima.

Original entry on oeis.org

0, 3, 1008, 172573, 24118698, 3148308323, 401420959948, 50776368194073, 6405835208453198, 807454401764399823, 101751780468757346448, 12821210170324927605573, 1615491145485759589239698, 203552595669637872843811323, 25647653984634161426074132948
Offset: 1

Views

Author

R. H. Hardin, Dec 06 2008

Keywords

Crossrefs

Programs

  • PARI
    \\ PeaksBySig defined in A334774.
    a(n) = {PeaksBySig(vector(n,i,4), [2])[1]/10} \\ Andrew Howroyd, May 12 2020
    
  • PARI
    concat(0, Vec(x^2*(3 + 375*x - 935*x^2 - 89275*x^3 - 63000*x^4) / ((1 - 5*x)^3*(1 - 35*x)^2*(1 - 126*x)) + O(x^15))) \\ Colin Barker, Jul 19 2020

Formula

From Colin Barker, Jul 19 2020: (Start)
G.f.: x^2*(3 + 375*x - 935*x^2 - 89275*x^3 - 63000*x^4) / ((1 - 5*x)^3*(1 - 35*x)^2*(1 - 126*x)).
a(n) = 211*a(n-1) - 13060*a(n-2) + 319850*a(n-3) - 3093125*a(n-4) + 12831875*a(n-5) - 19293750*a(n-6) for n>6.
(End)

Extensions

Terms a(8) and beyond from Andrew Howroyd, May 12 2020

A152506 1/5 of the number of permutations of 4 indistinguishable copies of 1..n with exactly 4 local maxima.

Original entry on oeis.org

0, 1, 3277, 2483739, 1156102209, 443469188267, 156475306087585, 53194863262703203, 17785402102372820321, 5902647043581987876939, 1952635794694419540863057, 645038537405519790637628675, 212955626342843141187623423793, 70288152907297654332280282998411
Offset: 1

Views

Author

R. H. Hardin, Dec 06 2008

Keywords

Crossrefs

Programs

  • PARI
    \\ PeaksBySig defined in A334774.
    a(n) = {PeaksBySig(vector(n,i,4), [3])[1]/5} \\ Andrew Howroyd, May 12 2020

Extensions

Terms a(8) and beyond from Andrew Howroyd, May 12 2020

A152507 1/5 of the number of permutations of 4 indistinguishable copies of 1..n with exactly 5 local maxima.

Original entry on oeis.org

0, 0, 1268, 5299607, 8184246829, 8518545179048, 7375381060406666, 5823800163847281553, 4385124494281967244359, 3220844410144729325085834, 2335142573256061888321206228, 1681577911560502131835994578291, 1206702021031355908214429714812273
Offset: 1

Views

Author

R. H. Hardin, Dec 06 2008

Keywords

Crossrefs

Programs

  • PARI
    \\ PeaksBySig defined in A334774.
    a(n) = {PeaksBySig(vector(n,i,4), [4])[1]/5} \\ Andrew Howroyd, May 12 2020

Extensions

Terms a(8) and beyond from Andrew Howroyd, May 12 2020

A152508 1/10 of the number of permutations of 4 indistinguishable copies of 1..n with exactly 6 local maxima.

Original entry on oeis.org

0, 0, 42, 1836695, 10530242387, 29832986150825, 60695128902586540, 103817995457729295887, 161328267155502711433605, 237364194180589518867292325, 338385077937653019716292059598, 473635313924991038119333176290875, 655918703527056982804817522787817607
Offset: 1

Views

Author

R. H. Hardin, Dec 06 2008

Keywords

Crossrefs

Programs

  • PARI
    \\ PeaksBySig defined in A334774.
    a(n) = {PeaksBySig(vector(n,i,4), [5])[1]/10} \\ Andrew Howroyd, May 12 2020

Extensions

Terms a(8) and beyond from Andrew Howroyd, May 12 2020

A152510 1/60 of the number of permutations of 5 indistinguishable copies of 1..n with exactly 3 local maxima.

Original entry on oeis.org

0, 2, 1066, 328314, 87554515, 22414176982, 5672480870616, 1431066048773744, 360732335571459920, 90911141639422741152, 22910020941551289849856, 5773350885207751422091264, 1454885995214232796339050240, 366631366567387199476086758912, 92391110171365499708617443239936
Offset: 1

Views

Author

R. H. Hardin, Dec 06 2008

Keywords

Crossrefs

Programs

  • Mathematica
    LinearRecurrence[{382,-38020,1394280,-17690400,92123136,-170698752},{0,2,1066,328314,87554515,22414176982},20] (* Harvey P. Dale, Mar 14 2022 *)
  • PARI
    \\ PeaksBySig defined in A334774.
    a(n) = {PeaksBySig(vector(n,i,5), [2])[1]/60} \\ Andrew Howroyd, May 12 2020
    
  • PARI
    concat(0, Vec(x^2*(2 + 302*x - 2858*x^2 - 120673*x^3 - 71148*x^4) / ((1 - 6*x)^3*(1 - 56*x)^2*(1 - 252*x)) + O(x^20))) \\ Colin Barker, Jul 19 2020

Formula

From Colin Barker, Jul 19 2020: (Start)
G.f.: x^2*(2 + 302*x - 2858*x^2 - 120673*x^3 - 71148*x^4) / ((1 - 6*x)^3*(1 - 56*x)^2*(1 - 252*x)).
a(n) = 382*a(n-1) - 38020*a(n-2) + 1394280*a(n-3) - 17690400*a(n-4) + 92123136*a(n-5) - 170698752*a(n-6) for n>6.
(End)

Extensions

Terms a(7) and beyond from Andrew Howroyd, May 12 2020
Previous Showing 11-20 of 25 results. Next