A077936 Expansion of 1/(1 - 2*x - 2*x^2 - x^3).

1, 2, 6, 17, 48, 136, 385, 1090, 3086, 8737, 24736, 70032, 198273, 561346, 1589270, 4499505, 12738896, 36066072, 102109441, 289089922, 818464798, 2317218881, 6560457280, 18573817120, 52585767681, 148879626882, 421504606246, 1193354233937, 3378597307248

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• nonn
• easy

Comments

Row sum of A158687. - Paul Barry, Mar 24 2009

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (2,2,1).

Programs

Magma

I:=[1,2,6]; [n le 3 select I[n] else 2*Self(n-1)+2*Self(n-2)+Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jul 06 2015

Mathematica

CoefficientList[Series[1/(1-2*x-2*x^2-x^3),{x,0,40}],x] (* or *) LinearRecurrence[{2,2,1},{1,2,6},40] (* Vladimir Joseph Stephan Orlovsky, Jan 30 2012 *)

PARI

Vec(1/(1-2*x-2*x^2-x^3)+O(x^99)) \\ Charles R Greathouse IV, Jan 31 2012

Formula

a(n) = Sum_{k=0..n} Sum_{j=0..n-k} C(n-j,k)*C(2k,j). - Paul Barry, Mar 24 2009

a(n) = 2*a(n-1) + 2*a(n-2) + a(n-3) with a(0) = 1, a(1) = 2, a(2) = 6. - Taras Goy, Aug 04 2017