A015555 Expansion of x/(1 - 7*x - 2*x^2).

0, 1, 7, 51, 371, 2699, 19635, 142843, 1039171, 7559883, 54997523, 400102427, 2910712035, 21175189099, 154047747763, 1120684612539, 8152887783299, 59311583708171, 431486861523795, 3139031198082907, 22836192109627939

Offset: 0

Author

Olivier Gérard

Keywords

• nonn
• easy

Comments

For n>0, a(n) equals the number of words of length n-1 over {0,1,...,8} in which 0 and 1 avoid runs of odd lengths. - Milan Janjic, Jan 08 2017

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,2).

Programs

Magma

[n le 2 select n-1 else 7*Self(n-1) + 2*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 13 2012

Mathematica

Join[{a=0,b=1},Table[c=7*b+2*a;a=b;b=c,{n,100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 17 2011 *)
LinearRecurrence[{7, 2}, {0, 1}, 30] (* Vincenzo Librandi Nov 13 2012 *)
CoefficientList[Series[x/(1-7x-2x^2),{x,0,20}],x] (* Harvey P. Dale, Mar 14 2025 *)

PARI

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

Sage

[lucas_number1(n,7,-2) for n in range(0, 21)] # Zerinvary Lajos, Apr 24 2009

Formula

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

E.g.f.: (exp(x*(7 + sqrt(57))/2) - exp(x*(7 - sqrt(57))/2))/sqrt(57). - Iain Fox, Dec 30 2017