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

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, 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, 4, 7, 5, 6, 6

Offset: 1

Author

Benoit Cloitre, Dec 02 2002

Keywords

• nonn

Links

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

Crossrefs

Cf. A077653, A079623, A079624, A080096, A088226.

Programs

Haskell

a077623 n = a077623_list !! (n-1)
a077623_list = 1 : 2 : 4 : zipWith3 (\u v w -> abs (w - v - u))
               a077623_list (tail a077623_list) (drop 2 a077623_list)
-- Reinhard Zumkeller, Oct 11 2014

Magma

m:=120;
A077623:=[n le 3 select 2^(n-1) else Abs(Self(n-1) - Self(n-2) - Self(n-3)): n in [1..m+5]];
[A077623[n]: n in [1..m]]; // G. C. Greubel, Sep 11 2024

Mathematica

a[n_]:= a[n]= If[n<4, 2^(n-1), Abs[a[n-1] -a[n-2] -a[n-3]]];
Table[a[n], {n,120}] (* G. C. Greubel, Sep 11 2024 *)

SageMath

@CachedFunction
def a(n): # a = A077623
    if n<4: return 2^(n-1)
    else: return abs(a(n-1)-a(n-2)-a(n-3))
[a(n) for n in range(1,121)] # G. C. Greubel, Sep 11 2024

Formula

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