A090727 a(n) = 16a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 16.

2, 16, 254, 4048, 64514, 1028176, 16386302, 261152656, 4162056194, 66331746448, 1057145886974, 16848002445136, 268510893235202, 4279326289318096, 68200709735854334, 1086932029484351248, 17322711762013765634, 276076456162735898896

Offset: 0

Author

Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Jan 18 2004

Keywords

• easy
• nonn

Comments

Numbers n such that (n^2-4)/7 is a square. - Colin Barker, Mar 17 2014

Links

• Tanya Khovanova, Recursive Sequences
• Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)
• Index entries for linear recurrences with constant coefficients, signature (16,-1).

Crossrefs

Cf. A080246.

Programs

Mathematica

a[0] = 2; a[1] = 16; a[n_] := 16a[n - 1] - a[n - 2]; Table[ a[n], {n, 0, 15}] (* Robert G. Wilson v, Jan 30 2004 *)
LinearRecurrence[{16, -1}, {2, 16}, 20] (* T. D. Noe, Mar 17 2014 *)

Sage

[lucas_number2(n,16,1) for n in range(0,20)] # Zerinvary Lajos, Jun 26 2008

Formula

a(n) = (8+sqrt(63))^n + (8-sqrt(63))^n.

a(n)^2 = a(2n) + 2.

G.f.: (2-16*x)/(1-16*x+x^2). - Philippe Deléham, Nov 02 2008

a(n) = 2 * A001081(n). - R. J. Mathar, Nov 30 2008

Extensions

More terms from Robert G. Wilson v, Jan 30 2004