cp's OEIS Frontend

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.

A081072 Fibonacci(4*n) + 3, or Fibonacci(2*n+2)*Lucas(2*n-2).

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%I A081072 #39 Jul 03 2025 10:56:39
%S A081072 3,6,24,147,990,6768,46371,317814,2178312,14930355,102334158,
%T A081072 701408736,4807526979,32951280102,225851433720,1548008755923,
%U A081072 10610209857726,72723460248144,498454011879267,3416454622906710,23416728348467688,160500643816367091,1100087778366101934
%N A081072 Fibonacci(4*n) + 3, or Fibonacci(2*n+2)*Lucas(2*n-2).
%D A081072 Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.
%H A081072 Paolo Xausa, <a href="/A081072/b081072.txt">Table of n, a(n) for n = 0..1000</a>
%H A081072 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-8,1).
%F A081072 a(n) = 8*a(n-1) - 8*a(n-2) + a(n-3).
%F A081072 From _R. J. Mathar_, Sep 03 2010: (Start)
%F A081072 G.f.: ( -3+18*x ) / ( (x-1)*(x^2-7*x+1) ).
%F A081072 a(n) = 3+A033888(n). (End)
%F A081072 a(n) = (A004187(n)+1)*3. - _Martin Ettl_, Nov 11 2012
%p A081072 with(combinat): for n from 0 to 40 do printf(`%d,`,fibonacci(4*n)+3) od: # _James Sellers_, Mar 05 2003
%t A081072 Fibonacci[4*Range[0, 25]] + 3 (* _Paolo Xausa_, Jul 03 2025 *)
%o A081072 (Magma) [Fibonacci(4*n)+3: n in [0..50]]; // _Vincenzo Librandi_, Apr 20 2011
%o A081072 (Maxima) makelist(fib(4*n)+3, n, 0, 30); /* _Martin Ettl_, Nov 11 2012 */
%o A081072 (PARI) Vec((-3+18*x)/((x-1)*(x^2-7*x+1)) + O(x^30)) \\ _Michel Marcus_, Dec 23 2014
%Y A081072 Cf. A000045 (Fibonacci numbers), A004187, A033888.
%K A081072 nonn,easy
%O A081072 0,1
%A A081072 _R. K. Guy_, Mar 04 2003