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 A081077 #32 Jul 02 2025 16:02:01
%S A081077 6,21,126,846,5781,39606,271446,1860501,12752046,87403806,599074581,
%T A081077 4106118246,28143753126,192900153621,1322157322206,9062201101806,
%U A081077 62113250390421,425730551631126,2918000611027446,20000273725560981
%N A081077 a(n) = Lucas(4*n+2) + 3, or Lucas(2*n)*Lucas(2*n+2).
%D A081077 Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.
%H A081077 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-8,1).
%F A081077 a(n) = 8a(n-1) - 8a(n-2) + a(n-3).
%F A081077 a(n) = A081067(n)+1. - _R. J. Mathar_, May 18 2007
%F A081077 G.f.: -3*(2-9*x+2*x^2)/(x-1)/(x^2-7*x+1) = -3/(x-1)+(-3*x+3)/(x^2-7*x+1). - _R. J. Mathar_, Nov 18 2007
%F A081077 Sum_{n>=0} 1/a(n) = sqrt(5)/10. - _Amiram Eldar_, Oct 05 2020
%p A081077 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 A081077 Table[LucasL[4*n + 2] + 3, {n, 0, 30}] (* _Amiram Eldar_, Oct 05 2020 *)
%o A081077 (PARI) Vec(-3*(2-9*x+2*x^2)/(x-1)/(x^2-7*x+1) + O(x^30)) \\ _Michel Marcus_, Dec 23 2014
%Y A081077 Cf. A000032 (Lucas numbers), A081067.
%K A081077 nonn,easy
%O A081077 0,1
%A A081077 _R. K. Guy_, Mar 04 2003
%E A081077 More terms from _James Sellers_, Mar 05 2003