A070432 Period 4: repeat [0, 1, 4, 1]; a(n) = n^2 mod 8.

0, 1, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 0

Offset

0,3

Comments

Multiplicative with a(2) = 4, a(2^e) = 0 if e >= 2, a(p^e) = 1 otherwise. - David W. Wilson, Jun 12 2005

Links

Table of n, a(n) for n=0..100.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1). - R. J. Mathar, Apr 20 2010

Formula

From R. J. Mathar, Apr 20 2010: (Start)

a(n) = a(n-4) for n > 3.

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

Dirichlet g.f.: zeta(s)*(1 + 4*2^(-s))*(1 - 2^(-s)). - R. J. Mathar, Mar 10 2011

a(n) = (n mod 2) + 4*floor(((n+1) mod 4)/3). - Gary Detlefs, Dec 29 2011

From Wesley Ivan Hurt, Mar 19 2015: (Start)

a(n) = (((n+1) mod 4) - 1)^2.

a(n) = (1 + (-1)^n - 2(-1)^((2n + 1 - (-1)^n)/4))^2/4. (End)

E.g.f.: 2*cosh(x) + sinh(x) - 2*cos(x). - G. C. Greubel, Mar 22 2016

a(n) = (3 + cos(n*Pi) - 4*cos(n*Pi/2))/2. - Wesley Ivan Hurt, Dec 21 2016

a(n) = a(-n) for all n in Z. - Michael Somos, Dec 22 2016

Example

G.f. = x + 4*x^2 + x^3 + x^5 + 4*x^6 + x^7 + x^9 + 4*x^10 + x^11 + x^13 + ...

Maple

seq(n mod 2 + 4*floor(((n+1) mod 4)/3), n = 0..200) # Gary Detlefs, Dec 29 2011

Mathematica

Table[Mod[n^2, 8], {n, 0, 99}] (* Vladimir Joseph Stephan Orlovsky, Apr 21 2011 *)
Mod[Range[0, 99]^2, 8] (* Alonso del Arte, Mar 20 2015 *)

Prog

(PARI) a(n)=n^2%8 \\ Charles R Greathouse IV, Oct 07 2015
(Magma) &cat [[0, 1, 4, 1]^^30]; // Wesley Ivan Hurt, Dec 21 2016

Crossrefs

Cf. A070430, A070431.

Sequence in context: A290459 A290458 A035253 * A170989 A290457 A344851

Adjacent sequences: A070429 A070430 A070431 * A070433 A070434 A070435

Keyword

nonn,easy,mult

Author

N. J. A. Sloane, May 12 2002

Status

approved