A097119 Expansion of (1-x)^2/((1-x)^3-2x^4).

1, 1, 1, 1, 3, 9, 21, 41, 75, 141, 281, 577, 1179, 2369, 4709, 9353, 18659, 37365, 74889, 149937, 299827, 599289, 1198101, 2396137, 4793051, 9587421, 19175449, 38349409, 76695403, 153388273, 306778917, 613566153, 1227140787, 2454279365

Offset: 0

Author

Paul Barry, Jul 25 2004

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-3,1,2).

Programs

Mathematica

CoefficientList[Series[(1-x)^2/((1-x)^3-2x^4),{x,0,50}],x]  (* Harvey P. Dale, Feb 25 2011 *)

Formula

G.f.: (1-2x+x^2)/(1-3x+3x^2-x^3-2x^4).

a(n) = 3a(n-1)-3a(n-2)+a(n-3)+2a(n-4).

a(n) = Sum_{k=0..floor(n/3)} binomial(n-k,3k)*2^k.