A015568 Expansion of x/(1 - 7*x - 10*x^2).

0, 1, 7, 59, 483, 3971, 32627, 268099, 2202963, 18101731, 148741747, 1222209539, 10042884243, 82522285091, 678084838067, 5571816717379, 45783565402323, 376203124990051, 3091257528953587, 25400833952575619, 208718412957565203, 1715037230228712611, 14092444741176640307

Offset: 0

Author

Olivier Gérard

Keywords

• nonn
• easy

Comments

Pisano period lengths: 1, 1, 8, 1, 4, 8, 12, 1, 24, 4, 5, 8, 21, 12, 8, 1, 16, 24, 45, 4, ... - R. J. Mathar, Aug 10 2012

Number of compositions of n-1 into parts 1 (of 7 sorts) and 2 (of 10 sorts). - Joerg Arndt, Oct 15 2013

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,10).

Programs

Magma

[n le 2 select n-1 else 7*Self(n-1) + 10*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 14 2012

Mathematica

LinearRecurrence[{7, 10}, {0, 1}, 30] (* Vincenzo Librandi, Nov 14 2012 *)
CoefficientList[Series[x/(1-7x-10x^2),{x,0,40}],x] (* Harvey P. Dale, Feb 06 2024 *)

PARI

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

Sage

[lucas_number1(n,7,-10) for n in range(0, 20)] # Zerinvary Lajos, Apr 24 2009

Formula

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

G.f.: Q(0)*x/(2-7*x), where Q(k) = 1 + 1/( 1 - x*(89*k-49)/( x*(89*k+40) - 14/Q(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Oct 14 2013