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 A152152 #41 Jan 05 2025 19:51:39
%S A152152 0,1,1,16,25,121,256,841,2025,5776,14641,39601,102400,271441,707281,
%T A152152 1860496,4862025,12752041,33362176,87403801,228765625,599074576,
%U A152152 1568239201,4106118241,10749542400,28143753121,73680216481,192900153616
%N A152152 a(n) = Product_{k=1..n} (1 + 4*sin(2*Pi*k/n)^2).
%H A152152 Seiichi Manyama, <a href="/A152152/b152152.txt">Table of n, a(n) for n = 0..2000</a>
%H A152152 M. Baake, J. Hermisson, and P. Pleasants, <a href="http://dx.doi.org/10.1088/0305-4470/30/9/016">The torus parametrization of quasiperiodic LI-classes</a>, J. Phys. A 30 (1997), no. 9, 3029-3056. See Table 4.
%H A152152 Kh. Bibak and M. H. Shirdareh Haghighi, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL12/Bibak/bibak4.html">Some Trigonometric Identities Involving Fibonacci and Lucas Numbers </a>, Journal of Integer Sequences, Vol. 12 (2009), Article 09.8.4
%H A152152 N. Garnier and O. Ramaré, <a href="https://ramare-olivier.github.io/Maths/CirculantFibonacci.pdf">Fibonacci numbers and trigonometric identities</a>, April 2006.
%H A152152 N. Garnier and O. Ramaré, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/46_47-1/Ramare_Garnier_11-08.pdf">Fibonacci numbers and trigonometric identities</a>, Fibonacci Quart. 46/47 (2008/2009), no. 1, 56-61.
%F A152152 a(n) = Product_{k=1..n} (1 + 4*sin(2*Pi*k/n)^2).
%F A152152 a(n) = (1 + Fibonacci(n) - 2*Fibonacci(n + 1) + (-1)^n)^2.
%F A152152 G.f.: -x*(x^6 -2*x^5 +10*x^4 -14*x^3 +10*x^2 -2*x +1)/((x -1)*(x +1)*(x^2 -3*x +1)*(x^2 -x -1)*(x^2 +x -1)). - _Colin Barker_, Apr 13 2014
%F A152152 a(n) = A001350(n)^2. - _Colin Barker_, Apr 13 2014
%F A152152 a(n) = (1 + (-1)^n - Lucas(n))^2. - _G. C. Greubel_, Mar 13 2019
%t A152152 Table[(1 + Fibonacci[n] - 2*Fibonacci[n+1] + (-1)^n)^2, {n, 0, 30}]
%o A152152 (PARI) {a(n) = (1-fibonacci(n-1)-fibonacci(n+1)+(-1)^n)^2}; \\ _G. C. Greubel_, Mar 13 2019
%o A152152 (Magma) [(1-Lucas(n)+(-1)^n)^2: n in [0..30]]; // _G. C. Greubel_, Mar 13 2019
%o A152152 (Sage) [(1-lucas_number2(n,1,-1)+(-1)^n)^2 for n in (0..30)] # _G. C. Greubel_, Mar 13 2019
%Y A152152 Cf. A000032, A001350, A324487.
%K A152152 nonn
%O A152152 0,4
%A A152152 _Roger L. Bagula_ and _Gary W. Adamson_, Nov 26 2008