A270824 Period 16: repeat [0, 1, 1, 0, 2, 3, 3, 2, 3, 2, 2, 3, 1, 0, 0, 1].

0, 1, 1, 0, 2, 3, 3, 2, 3, 2, 2, 3, 1, 0, 0, 1, 0, 1, 1, 0, 2, 3, 3, 2, 3, 2, 2, 3, 1, 0, 0, 1, 0, 1, 1, 0, 2, 3, 3, 2, 3, 2, 2, 3, 1, 0, 0, 1, 0, 1, 1, 0, 2, 3, 3, 2, 3, 2, 2, 3, 1, 0, 0, 1, 0, 1, 1, 0, 2, 3, 3, 2, 3, 2, 2, 3, 1, 0, 0, 1, 0, 1, 1, 0, 2, 3, 3, 2, 3, 2, 2, 3, 1, 0, 0, 1

Offset: 0

Author

William Walkington, Mar 23 2016

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,-1,1).

Crossrefs

Cf. A270823.

Programs

Mathematica

PadRight[{},120,{0,1,1,0,2,3,3,2,3,2,2,3,1,0,0,1}] (* Harvey P. Dale, Sep 16 2017 *)

PARI

a(n)=[0, 1, 1, 0, 2, 3, 3, 2, 3, 2, 2, 3, 1, 0, 0, 1][n%16+1] \\ Charles R Greathouse IV, Jul 17 2016

Formula

a(n) = (floor((n+4)/4) - [floor(n/4) + floor((n+4)/4)] * [(floor((n+12)/8)) mod 2 * (floor((n+3)/2)) mod 2 + (floor((n+4)/8)) mod 2 * (floor((n+1)/2)) mod 2]) mod 4.

From Chai Wah Wu, Jun 04 2016: (Start)

a(n) = a(n-1) - a(n-8) + a(n-9) for n > 8.

G.f.: x*(1 - x^2 + 2*x^3 + x^4 - x^6 + x^7)/((1 - x)*(1 + x^8)). (End)