A143432 Ultimately periodic length 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

0,5

Links

Table of n, a(n) for n=0..104.

Index entries for linear recurrences with constant coefficients, signature (1,-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)=(1/6)*{-2*(n mod 4)+[(n+1) mod 4]+4*[(n+2) mod 4]+[(n+3) mod 4]}-[C(2*n,n) mod 2]-{C[(n+1)^2,n+3] mod 2}, with n>=0 [From Paolo P. Lava, Aug 25 2008]

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

Mathematica

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

Prog

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

Crossrefs

Convolution inverse of A143431.

Sequence in context: A341698 A357069 A033461 * A137677 A015818 A225869

Adjacent sequences: A143429 A143430 A143431 * A143433 A143434 A143435

Keyword

nonn,easy

Author

Michael Somos, Aug 14 2008, Sep 18 2008

Status

approved