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A079623 a(1) = a(2) = 1, a(3)=4, a(n) = abs(a(n-1) - a(n-2) - a(n-3)).

%I A079623 #19 Sep 11 2024 12:23:31
%S A079623 1,1,4,2,3,3,2,4,1,5,0,6,1,5,2,4,3,3,4,2,5,1,6,0,7,1,6,2,5,3,4,4,3,5,
%T A079623 2,6,1,7,0,8,1,7,2,6,3,5,4,4,5,3,6,2,7,1,8,0,9,1,8,2,7,3,6,4,5,5,4,6,
%U A079623 3,7,2,8,1,9,0,10,1,9,2,8,3,7,4,6,5,5,6,4,7,3,8,2,9,1,10,0,11,1,10,2,9,3,8
%N A079623 a(1) = a(2) = 1, a(3)=4, a(n) = abs(a(n-1) - a(n-2) - a(n-3)).
%H A079623 Reinhard Zumkeller, <a href="/A079623/b079623.txt">Table of n, a(n) for n = 1..10000</a>
%F A079623 a(n*(n-10)) = 0.
%F A079623 Max( a(k) : 1<=k<=n) = floor(sqrt(n+24)).
%t A079623 nxt[{a_,b_,c_}]:={b,c,Abs[c-b-a]}; NestList[nxt,{1,1,4},110][[All,1]] (* _Harvey P. Dale_, Aug 12 2020 *)
%o A079623 (Haskell)
%o A079623 a079623 n = a079623_list !! (n-1)
%o A079623 a079623_list = 1 : 1 : 4 : zipWith3 (\u v w -> abs (w - v - u))
%o A079623                a079623_list (tail a079623_list) (drop 2 a079623_list)
%o A079623 -- _Reinhard Zumkeller_, Oct 11 2014
%o A079623 (Magma)
%o A079623 m:=120;
%o A079623 A079623:=[n le 3 select 4^Floor((n-1)/2) else Abs(Self(n-1) - Self(n-2) - Self(n-3)): n in [1..m+5]];
%o A079623 [A079623[n]: n in [1..m]]; // _G. C. Greubel_, Sep 11 2024
%o A079623 (SageMath)
%o A079623 @CachedFunction
%o A079623 def a(n): # a = A079623
%o A079623     if n<4: return 4^((n-1)//2)
%o A079623     else: return abs(a(n-1)-a(n-2)-a(n-3))
%o A079623 [a(n) for n in range(1,101)] # _G. C. Greubel_, Sep 11 2024
%Y A079623 Cf. A077623, A077653, A078108, A079624, A080096, A088226.
%K A079623 nonn
%O A079623 1,3
%A A079623 _Benoit Cloitre_, Jan 30 2003