A086594 a(n) = 8*a(n-1) + a(n-2), starting with a(0)=2 and a(1)=8.

2, 8, 66, 536, 4354, 35368, 287298, 2333752, 18957314, 153992264, 1250895426, 10161155672, 82540140802, 670482282088, 5446398397506, 44241669462136, 359379754094594, 2919279702218888, 23713617371845698, 192628218676984472, 1564739366787721474

Offset: 0

Author

Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Sep 11 2003

Keywords

• nonn
• easy

Comments

a(n+1)/a(n) converges to 4 + sqrt(17).

Examples

			a(4) = 8*a(3)+a(2) = 8*536+66 = 4354.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• 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 (8,1).

Crossrefs

Cf. A003285.

Programs

Magma

I:=[2,8]; [n le 2 select I[n] else 8*Self(n-1)+Self(n-2): n in [1..30]]; // Vincenzo Librandi, Sep 19 2016

Mathematica

LinearRecurrence[{8,1},{2,8},30] (* Harvey P. Dale, Sep 21 2014 *)
RecurrenceTable[{a[0] == 2, a[1] == 8, a[n] == 8 a[n-1] + a[n-2]}, a, {n, 30}] (* Vincenzo Librandi, Sep 19 2016 *)

PARI

x='x+O('x^30); Vec(2*(1-4*x)/(1-8*x-x^2)) \\ G. C. Greubel, Nov 07 2018

Formula

a(n) = (4+sqrt(17))^n + (4-sqrt(17))^n.

O.g.f: 2*(-1+4*x)/(-1+8*x+x^2). - R. J. Mathar, Dec 02 2007

a(n) = 2*A088317(n). - R. J. Mathar, Sep 27 2014