

A120714


Expansion of 2*(4*x^2+14*x+7)*x^2/((1x+x^2)*(6*x^3+10*x^2+2*x1)).


2



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

1,2


COMMENTS

Previous name was: Sequence produced by 7 X 7 Markov chain based on adjacency matrix of 7vertex graph with 10 edges, derived from the Fano plane.
Take the standard 7vertex 7edge 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(n2)+26a(n3)3a(n4)24a(n5)2a(n6)+6a(n7).
O.g.f.: 2*(4*x^2+14*x+7)*x^2/((1x+x^2)*(6*x^3+10*x^2+2*x1)).  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[n2]+26*a[n3]3*a[n4]24*a[n5]2*a[n6]+6*a[n7] 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



