A080096 a(1) = a(2) = 1, a(3) = 2, thereafter a(n) = abs(a(n-1) - a(n-2) - a(n-3)).

1, 1, 2, 0, 3, 1, 2, 2, 1, 3, 0, 4, 1, 3, 2, 2, 3, 1, 4, 0, 5, 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

Offset

1,3

Links

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

Formula

For n>=3 Max( a(k) : 1<=k<=n ) = floor ( sqrt(n+4)).

Special cases: a(n^2 + 4*n - 1) = 0 and a(n^2 - 4) = n.

a(A028557(n)) = a(A028557(n+1)).

Sum_{k=(n-1)^2 .. n^2} a(k) = n^2.

Mathematica

nxt[{a_, b_, c_}]:={b, c, Abs[c-b-a]}; NestList[nxt, {1, 1, 2}, 110][[All, 1]] (* Harvey P. Dale, Nov 14 2021 *)

Prog

(PARI) a(n)=local(k, m); if(n<1, 0, k=sqrtint(n+4); m=n+4-k^2; if(m%2, m\2+1, k-m\2))
(Haskell)
a080096 n = a080096_list !! (n-1)
a080096_list = 1 : 1 : 2 : zipWith3 (\u v w -> abs (w - v - u))
               a080096_list (tail a080096_list) (drop 2 a080096_list)
-- Reinhard Zumkeller, Oct 11 2014
(Magma)
m:=120;
A080096:=[n le 3 select Floor((n+1)/2) else Abs(Self(n-1) - Self(n-2) - Self(n-3)): n in [1..m+5]];
[A080096[n]: n in [1..m]]; // G. C. Greubel, Sep 11 2024
(SageMath)
@CachedFunction
def a(n): # a = A080096
    if n<4: return int((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

Crossrefs

Cf. A028347, A028557, A077623, A077653, A079623, A079624, A088226.

Sequence in context: A218585 A279507 A054656 * A322978 A294142 A068915

Adjacent sequences: A080093 A080094 A080095 * A080097 A080098 A080099

Keyword

nonn

Author

Benoit Cloitre, Jan 28 2003

Status

approved