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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 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.)