This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A164031 #14 Sep 08 2022 08:45:47
%S A164031 1,8,57,386,2549,16612,107493,692854,4456201,28626368,183771057,
%T A164031 1179304106,7566306749,48539073052,311365675293,1997258072734,
%U A164031 12811170195601,82174766283128,527090748332457,3380887858812626
%N A164031 a(n) = ((2+3*sqrt(2))*(5+sqrt(2))^n+(2-3*sqrt(2))*(5-sqrt(2))^n)/4.
%C A164031 Binomial transform of A164072. Fifth binomial transform of A164073.
%H A164031 G. C. Greubel, <a href="/A164031/b164031.txt">Table of n, a(n) for n = 0..1000</a>
%H A164031 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-23).
%F A164031 a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 1, a(1) = 8.
%F A164031 G.f.: (1-2*x)/(1-10*x+23*x^2).
%F A164031 E.g.f.: exp(5*x)*(2*cosh(sqrt(2)*x) + 3*sqrt(2)*sinh(sqrt(2)*x))/2. - _G. C. Greubel_, Apr 03 2018
%t A164031 CoefficientList[Series[(1 - 2*x)/(1 - 10*x + 23*x^2), {x,0,50}], x] (* or *) LinearRecurrence[{10,-23}, {1,8}, 50] (* _G. C. Greubel_, Sep 07 2017 *)
%o A164031 (Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((2+3*r)*(5+r)^n+(2-3*r)*(5-r)^n)/4: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Aug 09 2009
%o A164031 (PARI) x='x+O('x^50); Vec((1-2*x)/(1-10*x+23*x^2)) \\ _G. C. Greubel_, Sep 07 2017
%o A164031 (GAP) a:=[1,8];; for n in [3..25] do a[n]:=10*a[n-1]-23*a[n-2]; od; a; # _Muniru A Asiru_, Apr 04 2018
%Y A164031 Cf. A164072, A164073 (1, 3, 2, 6, 4, 12).
%K A164031 nonn
%O A164031 0,2
%A A164031 Al Hakanson (hawkuu(AT)gmail.com), Aug 08 2009
%E A164031 Edited and extended beyond a(5) by _Klaus Brockhaus_, Aug 09 2009