Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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