A078065 Expansion of (1-x)/(1+2*x+x^2+x^3).

1, -3, 5, -8, 14, -25, 44, -77, 135, -237, 416, -730, 1281, -2248, 3945, -6923, 12149, -21320, 37414, -65657, 115220, -202197, 354831, -622685, 1092736, -1917618, 3365185, -5905488, 10363409, -18186515, 31915109, -56007112, 98285630, -172479257, 302679996, -531166365, 932131991

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• sign
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-2,-1,-1).

Crossrefs

Cf. A005251.

Programs

Haskell

a078065 n = a078065_list !! n
a078065_list = 1 : zipWith (*) (cycle [-1, 1])
   (zipWith (+) (map (* 2) a005251_list) (map (* 3) $ drop 2 a005251_list))
-- Reinhard Zumkeller, Jul 13 2015

PARI

Vec((1-x)/(1+2*x+x^2+x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012

Formula

For n > 0: a(n) = (-1)^n * (2*A005251(n-1) + 3*A005251(n+2)). - Reinhard Zumkeller, Jul 13 2015

a(0) = 1, a(1) = -3, a(2) = 5, a(n) = -2*a(n-1) - a(n-2) - a(n-3) for n > 2. - Jinyuan Wang, Apr 07 2020