OFFSET
0,4
LINKS
Paul Barry, Symmetric Third-Order Recurring Sequences, Chebyshev Polynomials, and Riordan Arrays, JIS 12 (2009) 09.8.6.
Index entries for linear recurrences with constant coefficients, signature (0,7,0,-1).
FORMULA
a(n) = Product_{k=1..(n-1)/2} (5 + 4*cos(k*Pi/n)^2).
From Joerg Arndt, Jan 24 2013: (Start)
a(n) = 7*a(n-2) - a(n-4).
G.f.: (x^4 - x^3 - 6*x^2 + x + 1)/((x^2 - 3*x + 1)*(x^2 + 3*x + 1)). (End)
MATHEMATICA
a = Table[Product[5 + 4*Cos[k*Pi/n]^2, {k, 1, (n - 1)/2}], {n, 0, 10}]; FullSimplify[ExpandAll[a]]
Denominator[NestList[(5/(5+#))&, 0, 60]] (* Vladimir Joseph Stephan Orlovsky, Apr 13 2010 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula and Gary W. Adamson, Nov 24 2008
STATUS
approved