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A120714 Expansion of 2*(4*x^2+14*x+7)*x^2/((-1-x+x^2)*(6*x^3+10*x^2+2*x-1)). 2
0, 14, 42, 232, 974, 4522, 20180, 91422, 411782, 1858856, 8384078, 37827386, 170648724, 769875718, 3473203086, 15669055544, 70689396502, 318908566562, 1438725432052, 6490672907694, 29282051536966, 132103184740456 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

Table of n, a(n) for n=1..22.

Eric Weisstein's World of Mathematics, Fano Plane

Index entries for linear recurrences with constant coefficients, signature (0,15,26,-3,-24,-2,6).

FORMULA

a(n)=15a(n-2)+26a(n-3)-3a(n-4)-24a(n-5)-2a(n-6)+6a(n-7).

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

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 *)

CROSSREFS

Cf. A111384, A120715.

Sequence in context: A212514 A292051 A242897 * A041378 A302219 A302665

Adjacent sequences:  A120711 A120712 A120713 * A120715 A120716 A120717

KEYWORD

nonn,easy

AUTHOR

Roger L. Bagula, Aug 12 2006

EXTENSIONS

Edited by N. J. A. Sloane, Jul 14 2007, Jul 28 2007

New name using g.f. from Joerg Arndt, Sep 21 2021

STATUS

approved

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Last modified May 28 13:05 EDT 2022. Contains 354115 sequences. (Running on oeis4.)