A015559 Expansion of x/(1 - 7*x - 3*x^2).

0, 1, 7, 52, 385, 2851, 21112, 156337, 1157695, 8572876, 63483217, 470101147, 3481157680, 25778407201, 190892323447, 1413581485732, 10467747370465, 77514976050451, 574008074464552, 4250601449403217, 31476234369216175

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 (7,3).

Programs

Magma

[n le 2 select n-1 else 7*Self(n-1) + 3*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 14 2012

Mathematica

Join[{a=0,b=1},Table[c=7*b+3*a;a=b;b=c,{n,100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 17 2011 *)
LinearRecurrence[{7, 3}, {0, 1}, 30] (* Vincenzo Librandi, Nov 14 2012 *)
CoefficientList[Series[x/(1-7x-3x^2),{x,0,30}],x] (* Harvey P. Dale, Nov 12 2017 *)

PARI

x='x+O('x^30); concat([0], Vec(x/(1-7*x-3*x^2))) \\ G. C. Greubel, Dec 30 2017

Sage

[lucas_number1(n,7,-3) for n in range(0, 21)] # Zerinvary Lajos, Apr 24 2009

Formula

a(n) = 7*a(n-1) + 3*a(n-2).