A143432 Ultimately period 4 sequence [ 2, 2, 0, 0, ...] with a(0) = a(1) = 1.

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

Offset: 0

Author

Michael Somos, Aug 14 2008, Sep 18 2008

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (1,-1,1)

Crossrefs

Convolution inverse of A143431.

Programs

Mathematica

PadRight[{1,1},120,{2,2,0,0}] (* Harvey P. Dale, Feb 13 2016 *)

PARI

{a(n) = if(n<0, 0, n = n\2; if( n%2, 0, (n>1)+1 ))}

Formula

Euler transform of length 8 sequence [ 1, -1, 0, 2, 0, 0, 0, -1].

a(4*n + 2) = a(4*n + 3) = 0. a(4*n) = a(4*n + 1) = 2 unless n < 1.

G.f.: (1 + x^4) / ((1 - x) * (1 + x^2)).

a(n) = ((n+2) mod 4) - (n mod 2) - floor(3/(n+2)). - Wesley Ivan Hurt, Jun 30 2013