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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)).
3
0, 14, 42, 232, 974, 4522, 20180, 91422, 411782, 1858856, 8384078, 37827386, 170648724, 769875718, 3473203086, 15669055544, 70689396502, 318908566562, 1438725432052, 6490672907694, 29282051536966, 132103184740456
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
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
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 *)
PROG
(Magma) R<x>:=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
(SageMath)
def A120714_list(prec):
P.<x> = 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
CROSSREFS
Sequence in context: A212514 A292051 A242897 * A041378 A302219 A302665
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