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 A128533 #36 Sep 08 2022 08:45:30
%S A128533 0,4,7,22,54,145,376,988,2583,6766,17710,46369,121392,317812,832039,
%T A128533 2178310,5702886,14930353,39088168,102334156,267914295,701408734,
%U A128533 1836311902,4807526977,12586269024,32951280100,86267571271,225851433718,591286729878
%N A128533 a(n) = F(n)*L(n+2) where F=Fibonacci and L=Lucas numbers.
%C A128533 Generally, F(n)*L(n+k) = F(2*n + k) + F(k)*(-1)^(n+1): if k = 0 then sequence is A001906, if k = 1 it is A081714.
%H A128533 Vincenzo Librandi, <a href="/A128533/b128533.txt">Table of n, a(n) for n = 0..1000</a>
%H A128533 Mohammad K. Azarian, <a href="http://www.m-hikari.com/ijcms/ijcms-2012/45-48-2012/azarianIJCMS45-48-2012.pdf">Identities Involving Lucas or Fibonacci and Lucas Numbers as Binomial Sums</a>, International Journal of Contemporary Mathematical Sciences, Vol. 7, No. 45, 2012, pp. 2221-2227.
%H A128533 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-1).
%F A128533 a(n) = F(2*(n+1)) + (-1)^(n+1), assuming F(0) = 0 and L(0) = 2.
%F A128533 From _R. J. Mathar_, Apr 16 2009: (Start)
%F A128533 a(n) = 2*a(n-1) + 2*a(n-2) - a(n-3).
%F A128533 G.f.: x*(4-x)/((1+x)*(x^2-3*x+1)). (End)
%F A128533 a(n) = A186679(2*n). - _Reinhard Zumkeller_, Feb 25 2011
%F A128533 a(-n) = - A128535(n). - _Michael Somos_, May 26 2014
%F A128533 0 = a(n)*(+4*a(n) + a(n+1) - 17*a(n+2)) + a(n+1)*(-14*a(n+1) + a(n+2)) + a(n+2)*(+4*a(n+2)) for all n in Z. - _Michael Somos_, May 26 2014
%e A128533 a(4) = 54 because F(4)*L(6) = 3*18.
%e A128533 G.f. = 4*x + 7*x^2 + 22*x^3 + 54*x^4 + 145*x^5 + 376*x^6 + 988*x^7 + ...
%p A128533 with(combinat); A128533:=n->fibonacci(2*n+2)+(-1)^(n+1); seq(A128533(k),k=0..50); # _Wesley Ivan Hurt_, Oct 19 2013
%t A128533 LinearRecurrence[{2,2,-1}, {0,4,7}, 40] (* _Vincenzo Librandi_, Feb 20 2013 *)
%t A128533 a[n_]:= Fibonacci[2n+2] -(-1)^n; (* _Michael Somos_, May 26 2014 *)
%o A128533 (Magma) [Fibonacci(n)*Lucas(n+2): n in [0..30]]; // _Vincenzo Librandi_, Feb 20 2013
%o A128533 (PARI) vector(30, n, n--; fibonacci(2*(n+1)) + (-1)^(n+1)) \\ _G. C. Greubel_, Jan 07 2019
%o A128533 (Sage) [fibonacci(2*(n+1)) + (-1)^(n+1) for n in (0..30)] # _G. C. Greubel_, Jan 07 2019
%o A128533 (GAP) List([0..30], n -> Fibonacci(2*(n+1)) + (-1)^(n+1)); # _G. C. Greubel_, Jan 07 2019
%Y A128533 Cf. A001906, A081714, A128534, A128535.
%K A128533 nonn,easy
%O A128533 0,2
%A A128533 _Axel Harvey_, Mar 08 2007
%E A128533 More terms from _Vincenzo Librandi_, Feb 20 2013