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A050935 a(n) = a(n-1) - a(n-3) with a(1)=0, a(2)=0, a(3)=1.

%I A050935 #35 Aug 11 2024 22:05:58
%S A050935 0,0,1,1,1,0,-1,-2,-2,-1,1,3,4,3,0,-4,-7,-7,-3,4,11,14,10,-1,-15,-25,
%T A050935 -24,-9,16,40,49,33,-7,-56,-89,-82,-26,63,145,171,108,-37,-208,-316,
%U A050935 -279,-71,245,524,595,350,-174,-769,-1119,-945,-176,943,1888,2064,1121,-767,-2831,-3952
%N A050935 a(n) = a(n-1) - a(n-3) with a(1)=0, a(2)=0, a(3)=1.
%C A050935 The Ze3 sums, see A180662, of triangle A108299 equal the terms of this sequence without the two leading zeros. [Johannes W. Meijer, Aug 14 2011]
%D A050935 R. Palmaccio, "Average Temperatures Modeled with Complex Numbers", Mathematics and Informatics Quarterly, pp. 9-17 of Vol. 3, No. 1, March 1993.
%H A050935 Reinhard Zumkeller, <a href="/A050935/b050935.txt">Table of n, a(n) for n = 1..10000</a>
%H A050935 José L. Ramírez, Víctor F. Sirvent, <a href="http://ami.ektf.hu/uploads/papers/finalpdf/AMI_45_from91to105.pdf">A note on the k-Narayana sequence</a>, Annales Mathematicae et Informaticae, 45 (2015) pp. 91-105.
%H A050935 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, -1).
%F A050935 From _Paul Barry_, Oct 20 2004: (Start)
%F A050935 G.f.: x^2/(1-x+x^3).
%F A050935 a(n+2) = Sum_{k=0..floor(n/3)} binomial(n-2*k, k)*(-1)^k. (End)
%F A050935 G.f.: Q(0)*x^2/2, where Q(k) = 1 + 1/(1 - x*(12*k-1 + x^2)/( x*(12*k+5 + x^2 ) - 1/Q(k+1) )); (continued fraction). - _Sergei N. Gladkovskii_, Sep 12 2013
%p A050935 A050935 := proc(n) option remember; if n <= 1 then 0 elif n = 2 then 1 else A050935(n-1)-A050935(n-3); fi; end: seq(A050935(n), n=0..61);
%t A050935 LinearRecurrence[{1,0,-1},{0,0,1},70] (* _Harvey P. Dale_, Jan 30 2014 *)
%o A050935 (Haskell)
%o A050935 a050935 n = a050935_list !! (n-1)
%o A050935 a050935_list = 0 : 0 : 1 : zipWith (-) (drop 2 a050935_list) a050935_list
%o A050935 -- _Reinhard Zumkeller_, Jan 01 2012
%o A050935 (PARI) a(n)=([0,1,0; 0,0,1; -1,0,1]^(n-1)*[0;0;1])[1,1] \\ _Charles R Greathouse IV_, Feb 06 2017
%Y A050935 When run backwards this gives a signed version of A000931.
%Y A050935 Cf. A099529.
%Y A050935 Apart from signs, essentially the same as A078013.
%Y A050935 Cf. A203400 (partial sums).
%K A050935 easy,nice,sign
%O A050935 1,8
%A A050935 Richard J. Palmaccio (palmacr(AT)pinecrest.edu), Dec 31 1999
%E A050935 Offset adjusted by _Reinhard Zumkeller_, Jan 01 2012