A090728 a(n) = 20*a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 20.

2, 20, 398, 7940, 158402, 3160100, 63043598, 1257711860, 25091193602, 500566160180, 9986232009998, 199224074039780, 3974495248785602, 79290680901672260, 1581839122784659598, 31557491774791519700, 629567996373045734402, 12559802435686123168340

Offset: 0

Author

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

Keywords

• easy
• nonn

Comments

Except for the first term, positive values of x (or y) satisfying x^2 - 20xy + y^2 + 396 = 0. - Colin Barker, Feb 28 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 (20,-1).

Crossrefs

Cf. A080959, A037035, A054877.

Cf. A001085.

Programs

Mathematica

a[0] = 2; a[1] = 20; a[n_] := 20a[n - 1] - a[n - 2]; Table[ a[n], {n, 0, 15}] (* Robert G. Wilson v, Jan 30 2004 *)

PARI

Vec((2-20*x)/(1-20*x+x^2) + O(x^100)) \\ Colin Barker, Feb 28 2014

Sage

[lucas_number2(n,20,1) for n in range(0,20)] # Zerinvary Lajos, Jun 27 2008

Formula

a(n) = p^n + q^n, where p = 10 + 3*sqrt(11) and q = 10 - 3*sqrt(11). - Tanya Khovanova, Feb 06 2007

G.f.: (2-20*x)/(1-20*x+x^2). - Philippe Deléham, Nov 02 2008

Extensions

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

More terms from Colin Barker, Feb 28 2014