A152119 a(n) = Product_{k=1..(n-1)/2} (5 + 4*cos(k*Pi/n)^2).

1, 1, 1, 6, 7, 41, 48, 281, 329, 1926, 2255, 13201, 15456, 90481, 105937, 620166, 726103, 4250681, 4976784, 29134601, 34111385, 199691526, 233802911, 1368706081, 1602508992, 9381251041, 10983760033, 64300051206, 75283811239

Offset: 0

Author

Roger L. Bagula and Gary W. Adamson, Nov 24 2008

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A004187 (bisection), A049685 (bisection).

Programs

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 *)
LinearRecurrence[{0,7,0,-1},{1,1,1,6,7},30] (* Harvey P. Dale, May 17 2025 *)

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)