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 A289414 #14 Jan 29 2025 11:19:29
%S A289414 1,10,110,1300,16100,205000,2651000,34570000,452810000,5944900000,
%T A289414 78145100000,1027861000000,13524161000000,177975730000000,
%U A289414 2342340110000000,30828986500000000,405769120100000000,5340773617000000000,70296251531000000000,925255405090000000000
%N A289414 a(n) = ((10-sqrt(10))^n + (10+sqrt(10))^n) / 2.
%H A289414 Colin Barker, <a href="/A289414/b289414.txt">Table of n, a(n) for n = 0..850</a>
%H A289414 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20,-90).
%F A289414 G.f.: (1 - 10*x) / (1 - 20*x + 90*x^2).
%F A289414 a(n) = 20*a(n-1) - 90*a(n-2) for n>1.
%p A289414 a:= n-> (<<0|1>, <-90|20>>^n. <<1,10>>)[1,1]:
%p A289414 seq(a(n), n=0..25); # _Alois P. Heinz_, Jul 06 2017
%t A289414 LinearRecurrence[{20, -90}, {1, 10}, 20] (* _Jean-François Alcover_, Jan 29 2025 *)
%o A289414 (PARI) Vec((1 - 10*x) / (1 - 20*x + 90*x^2) + O(x^25))
%Y A289414 Cf. A083881, A090139, A143079, A145301, A145302, A145303, A289415.
%K A289414 nonn,easy
%O A289414 0,2
%A A289414 _Colin Barker_, Jul 06 2017