A152104 - OEIS

%I #17 Sep 08 2022 08:45:39

%S 1,2,4,22,80,342,1364,5602,22720,92642,376884,1534742,6247120,

%T 25433302,103536164,421498242,1715905280,6985435522,28437573604,

%U 115768943702,471293442000,1918628145302,7810704140404,31797251383522

%N 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.

%C a(n+1)/a(n) tends to (1 + sqrt(11) + sqrt(2*(4+sqrt(11))))/2 = 4.070983928708143809... - _Vaclav Kotesovec_, Nov 30 2012

%H Vincenzo Librandi, <a href="/A152104/b152104.txt">Table of n, a(n) for n = 0..300</a>

%F 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

%t 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 *)

%t 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 *)

%o (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

%o (Magma) R<x>:=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

%o (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

%Y Cf. A152094, A152096.

%K nonn,easy

%O 0,2

%A _Roger L. Bagula_, Nov 24 2008