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%I #19 Sep 08 2022 08:45:12
%S 0,1,3,23,127,783,4655,28015,167919,1007855,6046447,36280047,
%T 217677551,1306070767,7836413679,47018503919,282110979823,
%U 1692665966319,10155995623151,60935974088431,365615843831535,2193695064387311
%N Expansion of x*(1-2*x)/((1-x)*(1+2*x)*(1-6*x)).
%C Number of walks of length n between adjacent vertices of the Johnson graph J(5,2).
%C 6^n = A091054(n) + 6*a(n) + 3*4*A091056(n).
%H G. C. Greubel, <a href="/A091055/b091055.txt">Table of n, a(n) for n = 0..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/JohnsonGraph.html">Johnson Graph</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,8,-12).
%F a(n) = (3*6^n - 5*(-2)^n + 2)/30.
%F E.g.f.: (3*exp(6*x) - 5*exp(-2*x) + 2*exp(x))/30. - _G. C. Greubel_, Dec 27 2019
%p seq( (3*6^n -5*(-2)^n +2)/30, n=0..30); # _G. C. Greubel_, Dec 27 2019
%t Table[(3*6^n -5*(-2)^n +2)/30, {n,0,30}] (* _G. C. Greubel_, Dec 27 2019 *)
%o (PARI) vector(31, n, (3*6^(n-1) -5*(-2)^(n-1) +2)/30) \\ _G. C. Greubel_, Dec 27 2019
%o (Magma) [(3*6^n -5*(-2)^n +2)/30: n in [0..30]]; // _G. C. Greubel_, Dec 27 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 25); [0] cat Coefficients(R!( x*(1-2*x)/((1-x)*(1+2*x)*(1-6*x)))); // _Marius A. Burtea_, Dec 30 2019
%o (Sage) [(3*6^n -5*(-2)^n +2)/30 for n in (0..30)] # _G. C. Greubel_, Dec 27 2019
%o (GAP) List([0..30], n-> (3*6^n -5*(-2)^n +2)/30); # _G. C. Greubel_, Dec 27 2019
%Y Cf. A091054, A091056.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Dec 17 2003
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