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 A081079 #36 Jul 02 2025 16:02:01
%S A081079 0,15,120,840,5775,39600,271440,1860495,12752040,87403800,599074575,
%T A081079 4106118240,28143753120,192900153615,1322157322200,9062201101800,
%U A081079 62113250390415,425730551631120,2918000611027440,20000273725560975
%N A081079 a(n) = Lucas(4*n+2) - 3 = 5*Fibonacci(2*n)*Fibonacci(2*n+2).
%D A081079 Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.
%H A081079 G. C. Greubel, <a href="/A081079/b081079.txt">Table of n, a(n) for n = 0..1000</a>
%H A081079 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-8,1).
%F A081079 a(n) = 8*a(n-1) - 8*a(n-2) + a(n-3).
%F A081079 From _R. J. Mathar_, Sep 03 2010: (Start)
%F A081079 a(n) = 15*A092521(n) = 5*A058038(n).
%F A081079 G.f.: 15*x/((1-x)*(1-7*x+x^2)). (End)
%F A081079 From _G. C. Greubel_, Jun 12 2025: (Start)
%F A081079 a(n) = 15*(-1)^n*A156088(n).
%F A081079 E.g.f.: exp(7*x/2)*( 3*cosh(3*sqrt(5)*x/2) - sqrt(5)*sinh(3*sqrt(5)*x/2) ) - 3*exp(x). (End)
%p A081079 luc := proc(n) option remember: if n=0 then RETURN(2) fi: if n=1 then RETURN(1) fi: luc(n-1)+luc(n-2): end: for n from 0 to 40 do printf(`%d,`,luc(4*n+2)-3) od: # _James Sellers_, Mar 05 2003
%t A081079 LinearRecurrence[{8,-8,1}, {0,15,120}, 20] (* _Jean-François Alcover_, Nov 29 2023 *)
%o A081079 (Magma)
%o A081079 A081079:= func< n | Lucas(4*n+2) -3 >; // _G. C. Greubel_, Jun 12 2025
%o A081079 (SageMath)
%o A081079 def A081079(n): return lucas_number2(4*n+2,1,-1) -3 # _G. C. Greubel_, Jun 12 2025
%Y A081079 Cf. A000032 (Lucas numbers), A000045 (Fibonacci numbers), A058038, A092521, A156088.
%K A081079 nonn,easy
%O A081079 0,2
%A A081079 _R. K. Guy_, Mar 04 2003