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

%I A078065 #11 Apr 07 2020 03:38:33
%S A078065 1,-3,5,-8,14,-25,44,-77,135,-237,416,-730,1281,-2248,3945,-6923,
%T A078065 12149,-21320,37414,-65657,115220,-202197,354831,-622685,1092736,
%U A078065 -1917618,3365185,-5905488,10363409,-18186515,31915109,-56007112,98285630,-172479257,302679996,-531166365,932131991
%N A078065 Expansion of (1-x)/(1+2*x+x^2+x^3).
%H A078065 Reinhard Zumkeller, <a href="/A078065/b078065.txt">Table of n, a(n) for n = 0..1000</a>
%H A078065 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-2,-1,-1).
%F A078065 For n > 0: a(n) = (-1)^n * (2*A005251(n-1) + 3*A005251(n+2)). - _Reinhard Zumkeller_, Jul 13 2015
%F A078065 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
%o A078065 (PARI) Vec((1-x)/(1+2*x+x^2+x^3)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 27 2012
%o A078065 (Haskell)
%o A078065 a078065 n = a078065_list !! n
%o A078065 a078065_list = 1 : zipWith (*) (cycle [-1, 1])
%o A078065    (zipWith (+) (map (* 2) a005251_list) (map (* 3) $ drop 2 a005251_list))
%o A078065 -- _Reinhard Zumkeller_, Jul 13 2015
%Y A078065 Cf. A005251.
%K A078065 sign,easy
%O A078065 0,2
%A A078065 _N. J. A. Sloane_, Nov 17 2002