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 A075155 #55 Feb 24 2025 23:16:58
%S A075155 8,1,27,64,343,1331,5832,24389,103823,438976,1860867,7880599,33386248,
%T A075155 141420761,599077107,2537716544,10749963743,45537538411,192900170952,
%U A075155 817138135549,3461452853383,14662949322176,62113250509227,263115950765039,1114577054530568
%N A075155 Cubes of Lucas numbers.
%H A075155 G. C. Greubel, <a href="/A075155/b075155.txt">Table of n, a(n) for n = 0..1000</a>
%H A075155 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 A075155 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,6,-3,-1).
%F A075155 a(n) = 3*(-1)^n*L(n) + L(3*n).
%F A075155 a(n) = (-1)^n*A075151(n).
%F A075155 a(n) = A000032(n)^3 = A000032(n) * A001254(n).
%F A075155 a(n) = L(n)*C(n)^2, L(n) = Lucas numbers (A000032), C(n) = reflected Lucas numbers (comment to A061084).
%F A075155 a(n) = 3*a(n-1) + 6*a(n-2) - 3*a(n-3) - a(n-4), n>=4.
%F A075155 G.f.: ( 8-23*x-24*x^2+x^3 )/( (x^2+4*x-1)*(x^2-x-1) ).
%F A075155 a(n) = 2*A001077(n) + 3*A061084(n+1). - _R. J. Mathar_, Nov 17 2011
%F A075155 a(n) = L(3*n) + (F(n+4) - F(n-4))*(-1)^n, n>3 and F(n)=A000045(n). - _J. M. Bergot_, Feb 09 2016
%F A075155 a(n) + Sum_{i=0..n+1} a(i) = 19/2 + (5/2)*L(3*n+2). - _Greg Dresden_, Feb 24 2025
%t A075155 CoefficientList[Series[(8 - 23*x - 24*x^2 + x^3)/((x^2 + 4*x - 1)*(x^2 - x - 1)), {x,0,50}], x] (* or *) Table[LucasL[n]^3, {n,0,30}] (* or *) LinearRecurrence[{3,6,-3,-1}, {8, 1, 27, 64}, 30] (* _G. C. Greubel_, Dec 21 2017 *)
%o A075155 (Magma) [ Lucas(n)^3 : n in [0..120]]; // _Vincenzo Librandi_, Apr 14 2011
%o A075155 (PARI) a(n)=(fibonacci(n-1)+fibonacci(n+1))^3 \\ _Charles R Greathouse IV_, Feb 09 2016
%o A075155 (Python)
%o A075155 from sympy import lucas
%o A075155 def a(n): return lucas(n)**3
%o A075155 print([a(n) for n in range(25)]) # _Michael S. Branicky_, Aug 01 2021
%Y A075155 Cf. A000032, A061084, A075150, A075151.
%Y A075155 Third row of array A103324.
%K A075155 easy,nonn
%O A075155 0,1
%A A075155 Mario Catalani (mario.catalani(AT)unito.it), Sep 06 2002
%E A075155 Simpler definition from _Ralf Stephan_, Nov 01 2004