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 1-3 of 3 results.

A286945 Number of maximal matchings in the ladder graph P_2 X P_n.

Original entry on oeis.org

1, 2, 5, 11, 24, 51, 109, 234, 503, 1081, 2322, 4987, 10711, 23006, 49415, 106139, 227976, 489669, 1051759, 2259072, 4852259, 10422163, 22385754, 48082339, 103276009, 221826440, 476460797, 1023389687, 2198137722, 4721377893, 10141043023, 21781936530
Offset: 1

Views

Author

Andrew Howroyd, May 16 2017

Keywords

Links

Crossrefs

Cf. A284703, A284710, A286911.

Programs

  • GAP
    a:=[1,2,5,11,24];; for n in [6..35] do a[n]:=2*a[n-1]+a[n-4]+a[n-5]; od; a; # G. C. Greubel, Dec 30 2019
  • Magma
    R:=PowerSeriesRing(Integers(), 35); Coefficients(R!( x*(1+x^2+x^3+x^4)/(1-2*x-x^4-x^5) )); // G. C. Greubel, Dec 30 2019
  • Maple
    seq(coeff(series(x*(1+x^2+x^3+x^4)/(1-2*x-x^4-x^5), x, n+1), x, n), n = 1..35); # G. C. Greubel, Dec 30 2019
  • Mathematica
    Table[3Cos[nPi/3]/13 - 5Sin[nPi/3]/(13 Sqrt[3]) + RootSum[-1 -2# -#^2 +#^3 &, (-6 -72# +80#^2) #^n &]/403, {n, 35}] (* Eric W. Weisstein, Jul 13 2017 *)
LinearRecurrence[{2,0,0,1,1}, {1,2,5,11,24}, 35] (* Eric W. Weisstein, Jul 13 2017 *)
CoefficientList[Series[(1+x^2+x^3+x^4)/(1-2x-x^4-x^5), {x, 0, 35}], x] (* Eric W. Weisstein, Jul 13 2017 *)
  • PARI
    Vec((1+x^2+x^3+x^4)/((1-x+x^2)*(1-x-2*x^2-x^3)) + O(x^35))
  • Sage
    def A286945_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( x*(1+x^2+x^3+x^4)/(1-2*x-x^4-x^5) ).list()
a=A286945_list(35); a[1:] # G. C. Greubel, Dec 30 2019

Formula

a(n) = 2*a(n-1) + a(n-4) + a(n-5) for n>5.
G.f.: x*(1+x^2+x^3+x^4)/((1-x+x^2)*(1-x-2*x^2-x^3)).

A284701 Number of maximal matchings in the n-antiprism graph.

Original entry on oeis.org

2, 6, 14, 46, 137, 354, 905, 2366, 6278, 16681, 44156, 116650, 308180, 814645, 2153984, 5695102, 15056494, 39804582, 105231559, 278204561, 735502187, 1944477640, 5140687360, 13590620330, 35930023287, 94989547620, 251127430313, 663914974741
Offset: 1

Views

Author

Eric W. Weisstein, Apr 01 2017

Keywords

Comments

Sequence extrapolated to n=1 using recurrence. - Andrew Howroyd, May 16 2017

Links

Crossrefs

Cf. A284703, A284710, A192742, A284700.

Programs

  • Mathematica
    LinearRecurrence[{2, 1, 0, 3, 5, 1, -2, -1}, {2, 6, 14, 46, 137, 354,
  905, 2366}, 20] (* Eric W. Weisstein, May 17 2017 *)
CoefficientList[Series[x*(-8*x^7-14*x^6+6*x^5+25*x^4+12*x^3+2*x+2)/(x^8 +2*x^7-x^6-5*x^5 -3*x^4-x^2-2*x+1), {x, 0, 50}], x] (* G. C. Greubel, May 17 2017 *)
Table[RootSum[1 + 2 # - #^2 - 5 #^3 - 3 #^4 - #^6 - 2 #^7 + #^8 &, #^n &], {n, 10}] (* Eric W. Weisstein, May 26 2017 *)
  • PARI
    Vec((-8*x^7-14*x^6+6*x^5+25*x^4+12*x^3+2*x+2)/(x^8+2*x^7-x^6-5*x^5-3*x^4-x^2-2*x+1)+O(x^20)) \\ Andrew Howroyd, May 16 2017

Formula

From Andrew Howroyd, May 16 2017 (Start)
a(n) = 2*a(n-1) + a(n-2) + 3*a(n-4) + 5*a(n-5) + a(n-6) - 2*a(n-7) - a(n-8) for n>8.
G.f.: x*(-8*x^7 - 14*x^6 + 6*x^5 + 25*x^4 + 12*x^3 + 2*x + 2)/(x^8 + 2*x^7 - x^6 - 5*x^5 - 3*x^4 - x^2 - 2*x + 1). (End)

Extensions

a(1)-a(2) and a(16)-a(28) from Andrew Howroyd, May 16 2017

A287595 Number of maximal matchings in the n X n grid graph.

Original entry on oeis.org

1, 1, 2, 22, 400, 22228, 3136370, 1158560776, 1147204164108, 2980178704765860, 20513821200001569410, 373243563814532182524614, 17941038966060235808302667164
Offset: 0

Views

Author

Eric W. Weisstein, May 27 2017

Keywords

Links

Crossrefs

Main diagonal of A288026.
Cf. A286945, A288028, A099390, A242861, A284703.

Programs

  • Mathematica
    Join[{1}, Table[Length@FindIndependentVertexSet[LineGraph@GridGraph[{n, n}], Infinity, All], {n, 2, 6}]] (* Eric W. Weisstein, Jul 13 2024 *)

Extensions

a(7)-a(10) from Andrey Zabolotskiy, May 31 2017
a(1) changed and a(0) prepended by Alois P. Heinz, May 31 2017
a(11)-a(12) from Andrew Howroyd, Jun 04 2017
Showing 1-3 of 3 results.

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

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