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A266507 a(n) = 6*a(n - 1) - a(n - 2) with a(0) = 2, a(1) = 8.

%I A266507 #19 Sep 08 2022 08:46:15
%S A266507 2,8,46,268,1562,9104,53062,309268,1802546,10506008,61233502,
%T A266507 356895004,2080136522,12123924128,70663408246,411856525348,
%U A266507 2400475743842,13990997937704,81545511882382,475282073356588,2770146928257146,16145599496186288,94103450048860582
%N A266507 a(n) = 6*a(n - 1) - a(n - 2) with a(0) = 2, a(1) = 8.
%C A266507 Bisection of A078343 = A078343(2*n + 1).
%C A266507 Quadrisection of A266504 = A266504(4*n + 1).
%C A266507 Octasection of A266506 = A266506(8*n + 2).
%H A266507 G. C. Greubel, <a href="/A266507/b266507.txt">Table of n, a(n) for n = 0..1000</a>
%H A266507 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-1).
%F A266507 a(n) = (-sqrt(2)*(1+sqrt(2))^(2*n+1) - 3 *(1-sqrt(2))^(2*n+1) - sqrt(2)*(1-sqrt(2))^(2*n+1) + 3*(1+sqrt(2))^(2*n+1))/sqrt(8).
%F A266507 G.f.: 2*(1-2*x) / (1-6*x+x^2). - _Colin Barker_, Dec 31 2015
%t A266507 LinearRecurrence[{6, -1}, {2, 8}, 70] (* _Vincenzo Librandi_, Dec 31 2015 *)
%t A266507 Table[SeriesCoefficient[2 (1 - 2 x)/(1 - 6 x + x^2), {x, 0, n}], {n, 0, 22}] (* _Michael De Vlieger_, Dec 31 2015 *)
%o A266507 (Magma) I:=[2,8]; [n le 2 select I[n] else 6*Self(n-1)-Self(n-2): n in [1..70]]; // _Vincenzo Librandi_, Dec 31 2015
%o A266507 (PARI) Vec(2*(1-2*x)/(1-6*x+x^2) + O(x^30)) \\ _Colin Barker_, Dec 31 2015
%Y A266507 Bisection of A078343 = A078343(2n + 1).
%Y A266507 Quadrisection of A266504 = A266504(4n + 1).
%Y A266507 Octasection of A266506 = A266506(8n + 2).
%Y A266507 Equals 2*A038723(n).
%K A266507 nonn,easy
%O A266507 0,1
%A A266507 _Raphie Frank_, Dec 30 2015