A088226 a(1)=0, a(2)=0, a(3)=1; for n>3, a(n) = abs(a(n-1) - a(n-2) - a(n-3)).

0, 0, 1, 1, 0, 2, 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

Offset: 1

Author

Benoit Cloitre, Nov 04 2003

Keywords

• nonn

Comments

Conjecture: a(n) = m/2 where m is the smallest even distance from n to a square. - Ralf Stephan, Sep 23 2013

Links

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

Crossrefs

Cf. A077623, A077653, A079623, A079624, A080096.

Programs

Haskell

a088226 n = a088226_list !! (n-1)
a088226_list = 0 : 0 : 1 : zipWith3 (\u v w -> abs (w - v - u))
               a088226_list (tail a088226_list) (drop 2 a088226_list)
-- Reinhard Zumkeller, Oct 11 2014

Magma

m:=120;
A088226:=[n le 3 select Floor((n-1)/2) else Abs(Self(n-1) - Self(n-2) - Self(n-3)): n in [1..m+5]];
[A088226[n]: n in [1..m]]; // G. C. Greubel, Sep 11 2024

Mathematica

RecurrenceTable[{a[1]==a[2]==0,a[3]==1,a[n]==Abs[a[n-1]-a[n-2]-a[n-3]]},a,{n,110}] (* Harvey P. Dale, Apr 13 2012 *)

PARI

a(n)=t=sqrtint(n);if((n-t*t)%2==0,(n-t*t)/2,((t+1)^2-n)/2) \\ Ralf Stephan, Sep 23 2013

SageMath

@CachedFunction
def a(n): # a = A088226
    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

Formula

a(k^2 + 2*m + 2) = k-m and a(k^2 + 2*m + 1) = m, for k >= 0 and 0 <= m <= k.