A152104 Quartic product sequence: a(n) = 2^n*Product_{k=1..(n-1)/2} (1 + m*cos(k*Pi/n)^2 + q*cos(k*Pi/n)^4), with m=6, q=4.

1, 2, 4, 22, 80, 342, 1364, 5602, 22720, 92642, 376884, 1534742, 6247120, 25433302, 103536164, 421498242, 1715905280, 6985435522, 28437573604, 115768943702, 471293442000, 1918628145302, 7810704140404, 31797251383522

Offset: 0

Author

Roger L. Bagula, Nov 24 2008

Keywords

• nonn
• easy

Comments

a(n+1)/a(n) tends to (1 + sqrt(11) + sqrt(2*(4+sqrt(11))))/2 = 4.070983928708143809... - Vaclav Kotesovec, Nov 30 2012

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A152094, A152096.

Programs

Magma

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 1+2*(1-x)*x*(1+x)/(1-2*x-8*x^2-2*x^3+x^4) )); // G. C. Greubel, May 15 2019

Mathematica

With[{m = 6, q = 4}, Table[2^n*Round[Product[1 + m*Cos[k*Pi/n]^2 + q*Cos[k*Pi/n]^4, {k, 1, (n - 1)/2}]], {n, 0, 30}]] (* modified by G. C. Greubel, May 15 2019 *)
CoefficientList[Series[1+2*(1-x)*x*(1+x)/(1-2*x-8*x^2-2*x^3+x^4), {x, 0, 20}], x] (* Vaclav Kotesovec, Nov 30 2012 *)

PARI

my(x='x+O('x^30)); Vec(1+2*(1-x)*x*(1+x)/(1-2*x-8*x^2-2*x^3+x^4)) \\ G. C. Greubel, May 15 2019

Sage

(1+2*(1-x)*x*(1+x)/(1-2*x-8*x^2-2*x^3+x^4)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 15 2019

Formula

G.f.: 1 + 2*(1-x)*x*(1+x)/(1-2*x-8*x^2-2*x^3+x^4). - Vaclav Kotesovec, Nov 30 2012