OFFSET
1,1
COMMENTS
A159678 gives the y-values of solutions to the Diophantine equation x^2 - 7*y^2 = 2.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..750
Index entries for linear recurrences with constant coefficients, signature (16,-1).
FORMULA
a(1)=3, a(2)=45, a(n) = 16*a(n-1) - a(n-2).
a(n) = A041008(4n-2). - Robert Israel, Jan 05 2016
From R. J. Mathar, Jan 12 2016: (Start)
G.f.: 3*x*(1-x) / ( 1-16*x+x^2 ).
a(n) = 3*A157456(n). (End)
From G. C. Greubel, Jun 25 2022: (Start)
a(n) = 3*(ChebyshevU(n-1, 8) - ChebyshevU(n-2, 8)).
E.g.f.: exp(8*x)*(3*cosh(3*sqrt(7)*x) - sqrt(7)*sinh(3*sqrt(7)*x)) - 3. (End)
MATHEMATICA
LinearRecurrence[{16, -1}, {3, 45}, 20 ]
PROG
(PARI) lista(nn) = {print1(x = 3, ", "); print1(y = 45, ", "); for (n=2, nn, z = 16*y - x; print1(z, ", "); x = y; y = z; ); } \\ Michel Marcus, Jan 05 2016
(Magma) [n: n in [1..2*10^7] | IsSquare((n^2-2)/7)]; // Vincenzo Librandi, Jan 06 2016
(SageMath) [3*(chebyshev_U(n-1, 8) - chebyshev_U(n-2, 8)) for n in (1..30)] # G. C. Greubel, Jun 25 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Sture Sjöstedt, Jan 03 2016
STATUS
approved