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A077623 a(1)=1, a(2)=2, a(3)=4, a(n) = abs(a(n-1) - a(n-2) - a(n-3)).

%I A077623 #14 Sep 11 2024 10:08:35
%S A077623 1,2,4,1,5,0,6,1,5,2,4,3,3,4,2,5,1,6,0,7,1,6,2,5,3,4,4,3,5,2,6,1,7,0,
%T A077623 8,1,7,2,6,3,5,4,4,5,3,6,2,7,1,8,0,9,1,8,2,7,3,6,4,5,5,4,6,3,7,2,8,1,
%U A077623 9,0,10,1,9,2,8,3,7,4,6,5,5,6,4,7,3,8,2,9,1,10,0,11,1,10,2,9,3,8,4,7,5,6,6
%N A077623 a(1)=1, a(2)=2, a(3)=4, a(n) = abs(a(n-1) - a(n-2) - a(n-3)).
%H A077623 Reinhard Zumkeller, <a href="/A077623/b077623.txt">Table of n, a(n) for n = 1..10000</a>
%F A077623 a(n)/sqrt(n) is bounded. More precisely, let M(n) = Max ( a(k) : 1<=k<=n ); then M(n) = floor(sqrt(n+29)) for n>=4
%t A077623 a[n_]:= a[n]= If[n<4, 2^(n-1), Abs[a[n-1] -a[n-2] -a[n-3]]];
%t A077623 Table[a[n], {n,120}] (* _G. C. Greubel_, Sep 11 2024 *)
%o A077623 (Haskell)
%o A077623 a077623 n = a077623_list !! (n-1)
%o A077623 a077623_list = 1 : 2 : 4 : zipWith3 (\u v w -> abs (w - v - u))
%o A077623                a077623_list (tail a077623_list) (drop 2 a077623_list)
%o A077623 -- _Reinhard Zumkeller_, Oct 11 2014
%o A077623 (Magma)
%o A077623 m:=120;
%o A077623 A077623:=[n le 3 select 2^(n-1) else Abs(Self(n-1) - Self(n-2) - Self(n-3)): n in [1..m+5]];
%o A077623 [A077623[n]: n in [1..m]]; // _G. C. Greubel_, Sep 11 2024
%o A077623 (SageMath)
%o A077623 @CachedFunction
%o A077623 def a(n): # a = A077623
%o A077623     if n<4: return 2^(n-1)
%o A077623     else: return abs(a(n-1)-a(n-2)-a(n-3))
%o A077623 [a(n) for n in range(1,121)] # _G. C. Greubel_, Sep 11 2024
%Y A077623  Cf. A077653, A079623, A079624, A080096, A088226.
%K A077623 nonn
%O A077623 1,2
%A A077623 _Benoit Cloitre_, Dec 02 2002