A190510 a(n) = 8*a(n-1) + 4*a(n-2), with a(0)=0, a(1)=1.

0, 1, 8, 68, 576, 4880, 41344, 350272, 2967552, 25141504, 213002240, 1804583936, 15288680448, 129527779328, 1097376956416, 9297126768640, 78766521974784, 667320682872832, 5653631550881792, 47898335138545664, 405801207311892480, 3438002999049322496

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, May 24 2011

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,4).

Programs

Magma

I:=[0, 1]; [n le 2 select I[n] else 8*Self(n-1)+4*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 23 2011

Mathematica

LinearRecurrence[{8,4}, {0,1}, 50]

PARI

x='x+O('x^30); concat([0], Vec(x/(1-8*x-4*x^2))) \\ G. C. Greubel, Jan 24 2018

Formula

G.f.: x/(1 - 8*x - 4*x^2). - R. J. Mathar, Nov 21 2011

a(n+1) = Sum_{k, 0<=k<=n} A099089(n,k)*4^k. - Philippe Deléham, Nov 21 2011