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

0,1

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

Table of n, a(n) for n=0..17.

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).

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

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 *)

Prog

(Sage) [lucas_number2(n, 20, 1) for n in range(0, 20)] # Zerinvary Lajos, Jun 27 2008
(PARI) Vec((2-20*x)/(1-20*x+x^2) + O(x^100)) \\ Colin Barker, Feb 28 2014

Crossrefs

Cf. A080959, A037035, A054877.

Cf. A001085.

Sequence in context: A218306 A009236 A078698 * A210896 A090309 A002116

Adjacent sequences: A090725 A090726 A090727 * A090729 A090730 A090731

Keyword

easy,nonn

Author

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

Extensions

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

More terms from Colin Barker, Feb 28 2014

Status

approved