A015589 Expansion of x/(1 - 10*x - 7*x^2).

0, 1, 10, 107, 1140, 12149, 129470, 1379743, 14703720, 156695401, 1669880050, 17795668307, 189645843420, 2021028112349, 21537802027430, 229525217060743, 2446016784799440, 26066844367419601, 277790561167792090, 2960373522249858107, 31548269150673125700

Offset: 0

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..900
• Index entries for linear recurrences with constant coefficients, signature (10,7).

Crossrefs

Cf. A015579, A099371.

Programs

Magma

[n le 2 select n-1 else 10*Self(n-1) + 7*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 15 2012

Mathematica

Join[{a=0,b=1},Table[c=10*b+7*a;a=b;b=c,{n,60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2011 *)
CoefficientList[Series[x/(1-10x-7x^2),{x,0,30}],x] (* or *) LinearRecurrence[ {10,7},{0,1},31] (* Harvey P. Dale, Nov 26 2011 *)

PARI

x='x+O('x^30); concat([0], Vec(x/(1-10*x-7*x^2))) \\ G. C. Greubel, Jan 06 2018

Sage

[lucas_number1(n,10,-7) for n in range(0, 18)] # Zerinvary Lajos, Apr 26 2009

Formula

G.f.: x/(1 - 10*x - 7*x^2).

a(n) = 10*a(n-1) + 7*a(n-2).

a(n) = (8+5*sqrt(2))*((5+4*sqrt(2))^n-(5-4*sqrt(2))^n)/(16*(5+4*sqrt(2))). - Wesley Ivan Hurt, Aug 04 2025

Extensions

Extended by T. D. Noe, May 23 2011