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 1-2 of 2 results.

A091056 Expansion of x^2/((1-x)*(1+2*x)*(1-6*x)).

Original entry on oeis.org

0, 0, 1, 5, 33, 193, 1169, 6993, 42001, 251921, 1511697, 9069841, 54419729, 326517009, 1959104785, 11754623249, 70527750417, 423166480657, 2538998927633, 15233993478417, 91403961045265, 548423765922065
Offset: 0

Views

Author

Paul Barry, Dec 17 2003

Keywords

Comments

4*A091055(n) counts walks of length n between non-adjacent vertices of the Johnson graph J(5,2).
6^n = A091054(n) + 6*A091055(n) + 12*a(n).

Links

Crossrefs

Cf. A091054, A091055.

Programs

  • GAP
    List([0..40], n-> (3*6^n +5*(-2)^n -8)/120); # G. C. Greubel, Dec 27 2019
  • Magma
    [(3*6^n +5*(-2)^n -8)/120: n in [0..40]]; // G. C. Greubel, Dec 27 2019
  • Maple
    seq( (3*6^n +5*(-2)^n -8)/120, n=0..40); # G. C. Greubel, Dec 27 2019
  • Mathematica
    CoefficientList[Series[x^2/((1-x)(1+2x)(1-6x)),{x,0,40}],x] (* or *) LinearRecurrence[{5,8,-12},{0,0,1},40] (* Harvey P. Dale, Apr 02 2015 *)
  • PARI
    vector(41, n, (3*6^(n-1) + 5*(-2)^(n-1) - 8)/120) \\ G. C. Greubel, Dec 27 2019
  • Sage
    [(3*6^n +5*(-2)^n -8)/120 for n in (0..40)] # G. C. Greubel, Dec 27 2019

Formula

a(n) = (3 * 6^n + 5*(-2)^n - 8)/120.
a(0)=0, a(1)=0, a(2)=1, a(n) = 5*a(n-1) + 8*a(n-2) - 12*a(n-3). - Harvey P. Dale, Apr 02 2015
E.g.f.: (3*exp(6*x) + 5*exp(-2*x) - 8*exp(x))/120. - G. C. Greubel, Dec 27 2019

A091055 Expansion of x*(1-2*x)/((1-x)*(1+2*x)*(1-6*x)).

Original entry on oeis.org

0, 1, 3, 23, 127, 783, 4655, 28015, 167919, 1007855, 6046447, 36280047, 217677551, 1306070767, 7836413679, 47018503919, 282110979823, 1692665966319, 10155995623151, 60935974088431, 365615843831535, 2193695064387311
Offset: 0

Views

Author

Paul Barry, Dec 17 2003

Keywords

Comments

Number of walks of length n between adjacent vertices of the Johnson graph J(5,2).
6^n = A091054(n) + 6*a(n) + 3*4*A091056(n).

Links

Crossrefs

Cf. A091054, A091056.

Programs

  • GAP
    List([0..30], n-> (3*6^n -5*(-2)^n +2)/30); # G. C. Greubel, Dec 27 2019
  • Magma
    [(3*6^n -5*(-2)^n +2)/30: n in [0..30]]; // G. C. Greubel, Dec 27 2019
  • Magma
    R:=PowerSeriesRing(Integers(), 25); [0] cat  Coefficients(R!( x*(1-2*x)/((1-x)*(1+2*x)*(1-6*x)))); // Marius A. Burtea, Dec 30 2019
  • Maple
    seq( (3*6^n -5*(-2)^n +2)/30, n=0..30); # G. C. Greubel, Dec 27 2019
  • Mathematica
    Table[(3*6^n -5*(-2)^n +2)/30, {n,0,30}] (* G. C. Greubel, Dec 27 2019 *)
  • PARI
    vector(31, n, (3*6^(n-1) -5*(-2)^(n-1) +2)/30) \\ G. C. Greubel, Dec 27 2019
  • Sage
    [(3*6^n -5*(-2)^n +2)/30 for n in (0..30)] # G. C. Greubel, Dec 27 2019

Formula

a(n) = (3*6^n - 5*(-2)^n + 2)/30.
E.g.f.: (3*exp(6*x) - 5*exp(-2*x) + 2*exp(x))/30. - G. C. Greubel, Dec 27 2019
Showing 1-2 of 2 results.

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

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