A133874 n modulo 4 repeated 4 times.

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

Offset

0,5

Comments

Periodic with length 4^2 = 16.

Links

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

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

Formula

a(n) = (1 + floor(n/4)) mod 4.

a(n) = A010873(A002265(n+4)).

a(n) = 1 + floor(n/4) - 4*floor((n+4)/16).

a(n) = (((n+4) mod 16) - (n mod 4))/4.

a(n) = ((n + 4 - (n mod 4))/4) mod 4.

G.f. g(x) = (1 + x + x^2 + x^3 + 2x^4 + 2x^5 + 2x^6 + 2x^7 + 3x^8 + 3x^9 + 3x^10 + 3x^11)/(1-x^16).

G.f. g(x) = ((1-x^4)*(1+2x^4+3x^8))/((1-x)*(1-x^16)).

G.f. g(x) = (3x^16-4x^12+1)/((1-x)*(1-x^4)*(1-x^16)).

G.f. g(x) = (1+2x^4+3x^8)/((1-x)*(1+x^4)*(1+x^8)).

Mathematica

Flatten[Table[Table[Mod[n, 4], {4}], {n, 30}]] (* Harvey P. Dale, Dec 22 2013 *)

Prog

(Python)
def A133874(n): return 1+(n>>2)&3 # Chai Wah Wu, Jan 18 2023

Crossrefs

Cf. A000040, A133620-A133625, A133630, A038509, A133634-A133636.

Cf. A133884, A133880, A133890, A133900, A133910.

Sequence in context: A347648 A184320 A092363 * A053384 A321857 A186313

Adjacent sequences: A133871 A133872 A133873 * A133875 A133876 A133877

Keyword

nonn

Author

Hieronymus Fischer, Oct 10 2007

Status

approved