A079624 - OEIS

%I #13 Sep 11 2024 10:08:39

%S 1,1,6,4,3,7,0,10,3,7,6,4,9,1,12,2,11,3,10,4,9,5,8,6,7,7,6,8,5,9,4,10,

%T 3,11,2,12,1,13,0,14,1,13,2,12,3,11,4,10,5,9,6,8,7,7,8,6,9,5,10,4,11,

%U 3,12,2,13,1,14,0,15,1,14,2,13,3,12,4,11,5,10,6,9,7,8,8,7,9,6,10,5,11,4,12,3

%N a(1) = a(2) = 1, a(3) = 6, a(n) = abs(a(n-1) - a(n-2) - a(n-3)).

%H Reinhard Zumkeller, <a href="/A079624/b079624.txt">Table of n, a(n) for n = 1..10000</a>

%F For n >= 5, a(n^2 + 24*n - 13) = 0.

%F For n >= 38, Max( a(k) : 1<=k<=n) = floor(sqrt(n+156)).

%t a[n_]:= a[n]= If[n<4, 6^Floor[(n-1)/2], Abs[a[n-1] -a[n-2] -a[n-3]]];

%t Table[a[n], {n,100}] (* _G. C. Greubel_, Sep 11 2024 *)

%o (Haskell)

%o a079624 n = a079624_list !! (n-1)

%o a079624_list = 1 : 1 : 6 : zipWith3 (\u v w -> abs (w - v - u))

%o                a079624_list (tail a079624_list) (drop 2 a079624_list)

%o -- _Reinhard Zumkeller_, Oct 11 2014

%o (Magma)

%o m:=120;

%o A079624:=[n le 3 select 6^Floor((n-1)/2) else Abs(Self(n-1) - Self(n-2) - Self(n-3)): n in [1..m+5]];

%o [A079624[n]: n in [1..m]]; // _G. C. Greubel_, Sep 11 2024

%o (SageMath)

%o @CachedFunction

%o def a(n): # a = A079624

%o     if n<4: return 6^((n-1)//2)

%o     else: return abs(a(n-1)-a(n-2)-a(n-3))

%o [a(n) for n in range(1,101)] # _G. C. Greubel_, Sep 11 2024

%Y Cf. A077623, A077653, A078108, A079623, A080096, A088226.

%K nonn

%O 1,3

%A _Benoit Cloitre_, Jan 30 2003