A090730 a(n) = 22*a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 22.

2, 22, 482, 10582, 232322, 5100502, 111978722, 2458431382, 53973511682, 1184958825622, 26015120652002, 571147695518422, 12539234180753282, 275292004281053782, 6043884860002429922, 132690174915772404502

Offset

0,1

Links

Indranil Ghosh, Table of n, a(n) for n = 0..743

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 (22,-1).

Formula

a(n) = p^n + q^n, where p = 11 + 2*sqrt(30) and q = 11 - 2*sqrt(30). - Tanya Khovanova, Feb 06 2007

G.f.: (2-22*x)/(1-22*x+x^2). - Philippe Deléham, Nov 18 2008

a(n) = 2*A077422(n). - R. J. Mathar, Sep 27 2014

Mathematica

a[0] = 2; a[1] = 22; a[n_] := 22a[n - 1] - a[n - 2]; Table[ a[n], {n, 0, 15}] (* Robert G. Wilson v, Jan 30 2004 *)
LinearRecurrence[{22, -1}, {2, 22}, 20] (* Harvey P. Dale, Mar 07 2018 *)

Prog

(Sage) [lucas_number2(n, 22, 1) for n in range(0, 20)] # Zerinvary Lajos, Jun 26 2008

Crossrefs

Cf. A008951, A016005, A001613, A077422.

Sequence in context: A084949 A276454 A137076 * A090313 A110129 A328020

Adjacent sequences: A090727 A090728 A090729 * A090731 A090732 A090733

Keyword

easy,nonn

Author

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

Status

approved