|
%I #15 Feb 14 2021 05:53:24
%S 8,36,200,1156,6728,39204,228488,1331716,7761800,45239076,263672648,
%T 1536796804,8957108168,52205852196,304278005000,1773462177796,
%U 10336495061768,60245508192804,351136554095048,2046573816377476,11928306344169800
%N a(n) = sqrt( Product_{j=1..n} Product_{k=1..2} (4*sin((2*j-1)*Pi/(2*n))^2 + 4*sin((2*k-1)*Pi/2)^2) ).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7, -7, 1)
%F a(n) = 7*a(n-1) - 7*a(n-2) + a(n-3).
%F a(n) = 6*a(n-1) - a(n-2) - 8.
%F a(n) = 2*(A001541(n) + 1). - _Hugo Pfoertner_, Feb 14 2021
%F G.f.: 4*x*(2 - 5*x + x^2)/((1 - x)*(1 - 6*x + x^2)). - _Vaclav Kotesovec_, Feb 14 2021
%o (PARI) default(realprecision, 120);
%o a(n) = round(sqrt(prod(j=1, n, prod(k=1, 2, 4*sin((2*j-1)*Pi/(2*n))^2+4*sin((2*k-1)*Pi/2)^2))));
%Y Column k=2 of A341533.
%Y Cf. A001541.
%K nonn
%O 1,1
%A _Seiichi Manyama_, Feb 14 2021
|
