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%I #12 Sep 08 2022 08:45:12
%S 0,1,0,5,4,33,56,253,588,2105,5632,18261,52052,161617,473928,1443629,
%T 4287196,12948969,38672144,116365957,348398820,1046594561,3136987480,
%U 9416554845,28238479724,84737808793,254168687136,762595539893
%N Number of walks of length n between adjacent nodes on the Petersen graph.
%D N. Biggs, Algebraic Graph Theory, Cambridge, 2nd. Ed., 1993, p. 20.
%D F. Harary, Graph Theory, Addison-Wesley, 1969, p. 89.
%H G. C. Greubel, <a href="/A091001/b091001.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,5,-6).
%F G.f.: x*(1-2*x)/((1-x)*(1+2*x)*(1-3*x)).
%F a(n) = (3^(n+1) + (-2)^(n+3) + 5)/30.
%F 3^n = A091000(n) + 3*a(n) + 6*A091002(n).
%F a(n) = (A000244(n) - A001045(n+1)*(-1)^n - 6*A001045(n)*(-1)^n)/10.
%F a(n) = A091002(n+1) - 2*A091002(n). - _R. J. Mathar_, Oct 30 2014
%F E.g.f.: (3*exp(3*x) - 8*exp(-2*x) +5*exp(x))/30. - _G. C. Greubel_, Feb 01 2019
%t Table[(3^(n+1)+(-2)^(n+3)+5)/30, {n,0,30}] (* or *) LinearRecurrence[{2, 5,-6}, {0,1,0}, 30] (* _G. C. Greubel_, Feb 01 2019 *)
%o (PARI) vector(30, n, n--; (3^(n+1)+(-2)^(n+3)+5)/30) \\ _G. C. Greubel_, Feb 01 2019
%o (Magma) [(3^(n+1)+(-2)^(n+3)+5)/30: n in [0..30]]; // _G. C. Greubel_, Feb 01 2019
%o (Sage) [(3^(n+1)+(-2)^(n+3)+5)/30 for n in (0..30)] # _G. C. Greubel_, Feb 01 2019
%o (GAP) List([0..30], n -> (3^(n+1)+(-2)^(n+3)+5)/30) # _G. C. Greubel_, Feb 01 2019
%K easy,nonn
%O 0,4
%A _Paul Barry_, Dec 12 2003
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