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 A087404 #30 Mar 13 2025 11:07:56
%S A087404 2,4,26,124,626,3124,15626,78124,390626,1953124,9765626,48828124,
%T A087404 244140626,1220703124,6103515626,30517578124,152587890626,
%U A087404 762939453124,3814697265626,19073486328124,95367431640626,476837158203124,2384185791015626,11920928955078124,59604644775390626
%N A087404 a(n) = 4*a(n-1) + 5*a(n-2) for n > 1, with a(0) = 2 and a(1) = 4.
%C A087404 Let F(x) = Product_{n>=0} (1 - x^(3*n+1))/(1 - x^(3*n+2)). This sequence is the simple continued fraction expansion of the real number 1 + F(-1/5) = 2.24761 97788 60361 46849 ... = 2 + 1/(4 + 1/(26 + 1/(124 + 1/(626 + ...)))). See A111317. - _Peter Bala_, Dec 26 2012
%H A087404 Michael De Vlieger, <a href="/A087404/b087404.txt">Table of n, a(n) for n = 0..1430</a>
%H A087404 Weerayuth Nilsrakoo and Achariya Nilsrakoo, <a href="https://doi.org/10.37394/23206.2025.24.7">On One-Parameter Generalization of Jacobsthal Numbers</a>, WSEAS Trans. Math. (2025) Vol. 24, 51-61. See p. 3.
%H A087404 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,5).
%F A087404 G.f.: (2 - 4*x)/(1 - 4*x - 5*x^2).
%F A087404 a(n) = 5^n + (-1)^n.
%F A087404 From _Elmo R. Oliveira_, Aug 23 2024: (Start)
%F A087404 E.g.f.: exp(-x)*(exp(6*x) + 1).
%F A087404 a(n) = 2*A081340(n). (End)
%t A087404 CoefficientList[Series[(2 - 4x)/(1 - 4x - 5x^2), {x, 0, 25}], x]
%t A087404 LinearRecurrence[{4,5},{2,4},30] (* _Harvey P. Dale_, May 13 2022 *)
%o A087404 (Sage) [lucas_number2(n,4,-5) for n in range(0, 22)] # _Zerinvary Lajos_, May 14 2009
%Y A087404 Cf. A081340, A111317.
%K A087404 easy,nonn
%O A087404 0,1
%A A087404 Mario Catalani (mario.catalani(AT)unito.it), Sep 01 2003
%E A087404 a(22)-a(24) from _Elmo R. Oliveira_, Aug 23 2024