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 A152261 #13 May 23 2023 15:21:27
%S A152261 1,9,86,864,9016,96624,1054016,11628864,129214336,1442064384,
%T A152261 16136869376,180866755584,2029199527936,22779718078464,
%U A152261 255815761289216,2873425129242624,32279654468386816,362653470608523264
%N A152261 a(n) = ((9 + sqrt(5))^n + (9 - sqrt(5))^n)/2.
%C A152261 Binomial transform of A152109. - _Philippe Deléham_, Dec 03 2008
%H A152261 G. C. Greubel, <a href="/A152261/b152261.txt">Table of n, a(n) for n = 0..950</a>
%H A152261 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18,-76).
%F A152261 From _Philippe Deléham_, Dec 03 2008: (Start)
%F A152261 a(n) = 18*a(n-1) - 76*a(n-2), n > 1; a(0)=1, a(1)=9.
%F A152261 G.f.: (1-9*x)/(1-18*x+76*x^2).
%F A152261 a(n) = Sum_{k=0..n} A098158(n,k)*9^(2k-n)*5^(n-k). (End)
%F A152261 a(n) = m^n*(ChebyshevU(n, 9/m) - (9/m)*ChebyshevU(n-1, 9/m)), where m = 2*sqrt(19). - _G. C. Greubel_, May 23 2023
%t A152261 LinearRecurrence[{18,-76}, {1,9}, 41] (* _G. C. Greubel_, May 23 2023 *)
%o A152261 (Magma) Z<x>:= PolynomialRing(Integers()); N<r5>:=NumberField(x^2-5); S:=[ ((9+r5)^n+(9-r5)^n)/2: n in [0..17] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Dec 03 2008
%o A152261 (Magma) [n le 2 select 9^(n-1) else 18*Self(n-1) -76*Self(n-2): n in [1..30]]; // _G. C. Greubel_, May 23 2023
%o A152261 (SageMath)
%o A152261 @CachedFunction
%o A152261 def a(n): # a = A152261
%o A152261 if (n<2): return 9^n
%o A152261 else: return 18*a(n-1) -76*a(n-2)
%o A152261 [a(n) for n in range(41)] # _G. C. Greubel_, May 23 2023
%Y A152261 Cf. A152109.
%K A152261 nonn
%O A152261 0,2
%A A152261 Al Hakanson (hawkuu(AT)gmail.com), Dec 01 2008
%E A152261 Extended beyond a(6) by _Klaus Brockhaus_, Dec 03 2008