A131078 Periodic sequence (1, 1, 1, 1, 0, 0, 0, 0).

1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1

Offset: 1

Author

Klaus Brockhaus, following a suggestion of Paul Curtz, Jun 14 2007

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A131074, A000035.

Period 2*k: repeat k ones followed by k zeros: A000035(n+1) (k=1), A133872(n) (k=2), A088911 (k=3), this sequence (k=4), and A112713(n-1) (k=5).

Programs

Magma

m:=105; [ [1, 1, 1, 1, 0, 0, 0, 0][ (n-1) mod 8 + 1 ]: n in [1..m] ];

Magma

&cat[[1, 1, 1, 1, 0, 0, 0,0]: n in [0..10]]; // Vincenzo Librandi, May 31 2015

Magma

[Floor((1+(-1)^((2*n+11-(-1)^n+2*(-1)^((2*n+5-(-1)^n)/4))/8))/2): n in [1..60]]; // Vincenzo Librandi, May 31 2015

PARI

{m=105; for(n=1, m, print1((n-1)%8<4, ","))}

Python

def A131078(n): return int(not n-1&4) # Chai Wah Wu, Jan 31 2023

Formula

a(1) = a(2) = a(3) = a(4) = 1, a(5) = a(6) = a(7) = a(8) = 0; for n > 8, a(n) = a(n-8).

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

a(n) = floor(((n+4) mod 8)/4). [Gary Detlefs, May 17 2011]

From Wesley Ivan Hurt, May 30 2015: (Start)

a(n) = a(n-1)-a(n-4)+a(n-5), n>5.

a(n) = (1+(-1)^((2*n+11-(-1)^n+2*(-1)^((2*n+5-(-1)^n)/4))/8))/2. (End)

From Ridouane Oudra, Nov 17 2019: (Start)

a(n) = binomial(n+3,4) mod 2

a(n) = floor((n+3)/4) - 2*floor((n+3)/8). (End)