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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A120714 Expansion of 2*x^2*(7+14*x+4*x^2)/((1+x-x^2)*(1-2*x-10*x^2-6*x^3)).

Original entry on oeis.org

0, 14, 42, 232, 974, 4522, 20180, 91422, 411782, 1858856, 8384078, 37827386, 170648724, 769875718, 3473203086, 15669055544, 70689396502, 318908566562, 1438725432052, 6490672907694, 29282051536966, 132103184740456
Offset: 1

Views

Author

Roger L. Bagula, Aug 12 2006

Keywords

Comments

Previous name was: Sequence produced by 7 X 7 Markov chain based on adjacency matrix of 7-vertex graph with 10 edges, derived from the Fano plane.
Take the standard 7-vertex 7-edge Fano plane graph and add three edges that go around the triangle vertices from the middle of the sides ( connecting the middle of the sides without going through the center)
Characteristic polynomial is 6 - 2*x - 24*x^2 - 3*x^3 + 26*x^4 + 15*x^5 - x^7.

Links

Crossrefs

Cf. A111384, A120715.

Programs

  • Magma
    R:=PowerSeriesRing(Integers(), 30); [0] cat Coefficients(R!( 2*x^2*(7+14*x+4*x^2)/((1+x-x^2)*(1-2*x-10*x^2-6*x^3)) )); // G. C. Greubel, Jul 22 2023
  • Maple
    a[1]:=0: a[2]:=14: a[3]:=42: a[4]:=232: a[5]:=974: a[6]:=4522: a[7]:=20180: a[8]:=91422: for n from 9 to 25 do a[n]:=15*a[n-2]+26*a[n-3]-3*a[n-4]-24*a[n-5]-2*a[n-6]+6*a[n-7] end do: seq(a[n], n=1..25);
  • Mathematica
    LinearRecurrence[{0,15,26,-3,-24,-2,6},{0,14,42,232,974,4522,20180},30] (* Harvey P. Dale, Sep 20 2011 *)
  • SageMath
    def A120714_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 2*x^2*(7+14*x+4*x^2)/((1+x-x^2)*(1-2*x-10*x^2-6*x^3)) ).list()
a=A120714_list(30); a[1:] # G. C. Greubel, Jul 22 2023

Formula

a(n) = 15*a(n-2) +26*a(n-3) -3*a(n-4) -24*a(n-5) -2*a(n-6) +6*a(n-7).
O.g.f.: 2*x^2*(7+14*x+4*x^2)/((1+x-x^2)*(1-2*x-10*x^2-6*x^3)). - R. J. Mathar, Dec 05 2007

Extensions

Edited by N. J. A. Sloane, Jul 14 2007, Jul 28 2007
New name using g.f. from Joerg Arndt, Sep 21 2021
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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