|
|
REFERENCES
| Gareth Jones and David Singerman, Belyi Functions, Hypermaps and Galois Groups, Bull. London Math. Soc., 28 (1996), 561-590.
Henry MacKean and Victor Moll, Ellipic Curves, Cambridge University Press, New York, 1997, page 22
|
|
|
FORMULA
| G.f.: x(1+15x)/(1+14x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 16 2008] [Corrected by Richard Choulet (richardchoulet(AT)yahoo.fr), Nov 21 2008]
a(n)=(1/3)*sqrt(3)*[ -7+4*sqrt(3)]^n-(1/3)*sqrt(3)*[ -7-4*sqrt(3)]^n+(1/2)*[ -7-4*sqrt(3)]^n+(1 /2)*[ -7+4*sqrt(3)]^n [From Paolo P. Lava (paoloplava(AT)gmail.com), Nov 19 2008]
a(n)= ((3+2*sqrt(3))/6)*(-7+4*sqrt(3))^(n-1)+((3-2*sqrt(3))/6)*(-7-4*sqrt(3))^(n-1) (n>=1) [From Richard Choulet (richardchoulet(AT)yahoo.fr), Nov 21 2008]
a(n)=(-1)^n*A028230(n-1), n>1. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 19 2009]
a(n)=b such that (-1)^(2*n-3)*Integral_{x=0..Pi/2} cos((2*n-3)*x)/(2+sin(x)) dx = c + b*(ln(2)-ln(3)). [From Francesco Daddi (francesco.daddi(AT)libero.it), Aug 01 2011]
|
|
|
MATHEMATICA
| M = {{0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 1}, {-1, 0, 0, 0, -14, 0, 0, 0}}; v[1] = Table[1, {n, 1, 8}] v[n_] := v[n] = M.v[n - 1] a = Table[v[4*n][[1]], {n, 1, 25}]
|
