|
%I #17 Sep 08 2022 08:45:39
%S 1,1,1,11,37,179,869,3683,18389,80179,385029,1739651,8134709,37397203,
%T 173097317,799986979,3694294933,17085418099,78904394437,364797113027,
%U 1685324681973,7789441113619,35993781049381,166339303316579
%N Quartic product sequence: a(n) = Product_{k=1..floor((n-1)/2)} (1 + m*cos(k*Pi/n)^2 + q*cos(k*Pi/n)^4 ), with m = 2*4, q=2*4^3.
%C Limiting ratio at n=30: 4.621205928975311.
%C Exact value of this limit is (1 + sqrt(137) + sqrt(2*(5 + sqrt(137))))/4 = 4.621196599954103646539033792... - _Vaclav Kotesovec_, Nov 30 2012
%H Vincenzo Librandi, <a href="/A152094/b152094.txt">Table of n, a(n) for n = 0..300</a>
%F G.f.: 1 + x*(1-8*x^2)/(1-x-18*x^2-8*x^3+64*x^4). - _Vaclav Kotesovec_, Nov 30 2012
%t Table[Product[1 +8*Cos[k*Pi/n]^2 +128*Cos[k*Pi/n]^4, {k,1,(n-1)/2}], {n, 0, 30}]//Round (* modified by _G. C. Greubel_, May 08 2019 *)
%t CoefficientList[Series[1+x*(1-8*x^2)/(1-x-18*x^2-8*x^3+64*x^4), {x, 0, 23}], x] (* _Vaclav Kotesovec_, Nov 30 2012 *)
%o (PARI) my(x='x+O('x^30)); Vec(1 + x*(1-8*x^2)/(1-x-18*x^2-8*x^3+64*x^4)) \\ _G. C. Greubel_, May 08 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 1 + x*(1-8*x^2)/(1-x-18*x^2-8*x^3+64*x^4) )); // _G. C. Greubel_, May 08 2019
%o (Sage) (1 + x*(1-8*x^2)/(1-x-18*x^2-8*x^3+64*x^4)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, May 08 2019
%K nonn,easy
%O 0,4
%A _Roger L. Bagula_ and _Gary W. Adamson_, Nov 24 2008
|
