A090732 a(n) = 24a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 24.

2, 24, 574, 13752, 329474, 7893624, 189117502, 4530926424, 108553116674, 2600743873752, 62309299853374, 1492822452607224, 35765429562720002, 856877487052672824, 20529294259701427774, 491846184745781593752

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..723
• 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 (24,-1).

Crossrefs

Cf. A056949, A077424.

Programs

Mathematica

a[0] = 2; a[1] = 24; a[n_] := 24a[n - 1] - a[n - 2]; Table[ a[n], {n, 0, 15}] (* Robert G. Wilson v, Jan 30 2004 *)
LinearRecurrence[{24,-1},{2,24},30] (* Harvey P. Dale, Sep 19 2011 *)

PARI

a(n)=([0,1;-1,24]^n*[2;24])[1,1] \\ Charles R Greathouse IV, Feb 07 2017

Sage

[lucas_number2(n,24,1) for n in range(0,20)] # Zerinvary Lajos, Jun 26 2008

Formula

a(n) = p^n + q^n, where p = 12 + sqrt(143) and q = 12 - sqrt(143). - Tanya Khovanova, Feb 06 2007

G.f.: (2-24*x)/(1-24*x+x^2). - Philippe Deléham, Nov 02 2008

a(n)=2*A077424(n). - R. J. Mathar, Sep 27 2014