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

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, 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, 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

Offset: 1

Author

Benoit Cloitre, Jan 30 2003

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A077623, A077653, A078108, A079624, A080096, A088226.

Programs

Haskell

a079623 n = a079623_list !! (n-1)
a079623_list = 1 : 1 : 4 : zipWith3 (\u v w -> abs (w - v - u))
               a079623_list (tail a079623_list) (drop 2 a079623_list)
-- Reinhard Zumkeller, Oct 11 2014

Magma

m:=120;
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]];
[A079623[n]: n in [1..m]]; // G. C. Greubel, Sep 11 2024

Mathematica

nxt[{a_,b_,c_}]:={b,c,Abs[c-b-a]}; NestList[nxt,{1,1,4},110][[All,1]] (* Harvey P. Dale, Aug 12 2020 *)

SageMath

@CachedFunction
def a(n): # a = A079623
    if n<4: return 4^((n-1)//2)
    else: return abs(a(n-1)-a(n-2)-a(n-3))
[a(n) for n in range(1,101)] # G. C. Greubel, Sep 11 2024

Formula

a(n*(n-10)) = 0.

Max( a(k) : 1<=k<=n) = floor(sqrt(n+24)).