A015561 Expansion of x/(1 - 7*x - 4*x^2).

0, 1, 7, 53, 399, 3005, 22631, 170437, 1283583, 9666829, 72802135, 548282261, 4129184367, 31097419613, 234198674759, 1763780401765, 13283257511391, 100037924186797, 753398499353143, 5673941192219189, 42731182342946895

Offset: 0

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,4).

Programs

Magma

[n le 2 select n-1 else 7*Self(n-1) + 4*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 14 2012

Mathematica

Join[{a=0,b=1},Table[c=7*b+4*a;a=b;b=c,{n,100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 17 2011 *)
LinearRecurrence[{7, 4}, {0, 1}, 30] (* Vincenzo Librandi, Nov 14 2012 *)

PARI

x='x+O('x^30); concat([0], Vec(x/(1-7*x-4*x^2))) \\ G. C. Greubel, Dec 30 2017

Sage

[lucas_number1(n,7,-4) for n in range(0, 21)] # Zerinvary Lajos, Apr 24 2009

Formula

a(n) = 7*a(n-1) + 4*a(n-2).