Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #11 Apr 07 2020 03:38:33
%S 1,-3,5,-8,14,-25,44,-77,135,-237,416,-730,1281,-2248,3945,-6923,
%T 12149,-21320,37414,-65657,115220,-202197,354831,-622685,1092736,
%U -1917618,3365185,-5905488,10363409,-18186515,31915109,-56007112,98285630,-172479257,302679996,-531166365,932131991
%N Expansion of (1-x)/(1+2*x+x^2+x^3).
%H Reinhard Zumkeller, <a href="/A078065/b078065.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-2,-1,-1).
%F For n > 0: a(n) = (-1)^n * (2*A005251(n-1) + 3*A005251(n+2)). - _Reinhard Zumkeller_, Jul 13 2015
%F 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 (PARI) Vec((1-x)/(1+2*x+x^2+x^3)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 27 2012
%o (Haskell)
%o a078065 n = a078065_list !! n
%o a078065_list = 1 : zipWith (*) (cycle [-1, 1])
%o (zipWith (+) (map (* 2) a005251_list) (map (* 3) $ drop 2 a005251_list))
%o -- _Reinhard Zumkeller_, Jul 13 2015
%Y Cf. A005251.
%K sign,easy
%O 0,2
%A _N. J. A. Sloane_, Nov 17 2002