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 A163606 #16 Sep 08 2022 08:45:46
%S A163606 3,13,57,251,1107,4885,21561,95171,420099,1854397,8185689,36133355,
%T A163606 159500307,704068357,3107907993,13718969459,60558460803,267317978605,
%U A163606 1179998646009,5208766025819,22992605632851,101494271616373
%N A163606 a(n) = ((3 + 2*sqrt(2))*(3 + sqrt(2))^n + (3 - 2*sqrt(2))*(3 - sqrt(2))^n)/2.
%C A163606 Binomial transform of A048580. Inverse binomial transform of A163604.
%C A163606 For n >= 1, a(n-1) is the number of generalized compositions of n when there are 2^(i-1)+1 different types of i, (i=1,2,...). - _Milan Janjic_, Sep 24 2010
%H A163606 G. C. Greubel, <a href="/A163606/b163606.txt">Table of n, a(n) for n = 0..1000</a>
%H A163606 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6, -7).
%F A163606 a(n) = 6*a(n-1) - 7*a(n-2) for n > 1; a(0) = 3, a(1) = 13.
%F A163606 G.f.: (3-5*x)/(1-6*x+7*x^2).
%F A163606 E.g.f.: exp(3*x)*( 3*cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - _G. C. Greubel_, Jul 29 2017
%t A163606 LinearRecurrence[{6,-7},{3,13},40] (* _Harvey P. Dale_, Dec 24 2011 *)
%o A163606 (Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((3+2*r)*(3+r)^n+(3-2*r)*(3-r)^n)/2: n in [0..21] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Aug 07 2009
%o A163606 (PARI) x='x+O('x^50); Vec((3-5*x)/(1-6*x+7*x^2)) \\ _G. C. Greubel_, Jul 29 2017
%Y A163606 Cf. A048580, A163604.
%K A163606 nonn
%O A163606 0,1
%A A163606 Al Hakanson (hawkuu(AT)gmail.com), Aug 01 2009
%E A163606 Edited and extended beyond a(5) by _Klaus Brockhaus_, Aug 07 2009