OFFSET
0,4
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..2000
M. Baake, J. Hermisson, and P. Pleasants, The torus parametrization of quasiperiodic LI-classes, J. Phys. A 30 (1997), no. 9, 3029-3056. See Table 4.
Kh. Bibak and M. H. Shirdareh Haghighi, Some Trigonometric Identities Involving Fibonacci and Lucas Numbers , Journal of Integer Sequences, Vol. 12 (2009), Article 09.8.4
N. Garnier and O. Ramaré, Fibonacci numbers and trigonometric identities, April 2006.
N. Garnier and O. Ramaré, Fibonacci numbers and trigonometric identities, Fibonacci Quart. 46/47 (2008/2009), no. 1, 56-61.
FORMULA
a(n) = Product_{k=1..n} (1 + 4*sin(2*Pi*k/n)^2).
a(n) = (1 + Fibonacci(n) - 2*Fibonacci(n + 1) + (-1)^n)^2.
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
a(n) = A001350(n)^2. - Colin Barker, Apr 13 2014
a(n) = (1 + (-1)^n - Lucas(n))^2. - G. C. Greubel, Mar 13 2019
MATHEMATICA
Table[(1 + Fibonacci[n] - 2*Fibonacci[n+1] + (-1)^n)^2, {n, 0, 30}]
PROG
(PARI) {a(n) = (1-fibonacci(n-1)-fibonacci(n+1)+(-1)^n)^2}; \\ G. C. Greubel, Mar 13 2019
(Magma) [(1-Lucas(n)+(-1)^n)^2: n in [0..30]]; // G. C. Greubel, Mar 13 2019
(Sage) [(1-lucas_number2(n, 1, -1)+(-1)^n)^2 for n in (0..30)] # G. C. Greubel, Mar 13 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula and Gary W. Adamson, Nov 26 2008
STATUS
approved