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A070432 Period 4: repeat [0, 1, 4, 1]; a(n) = n^2 mod 8. 7
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 (list; graph; refs; listen; history; text; internal format)
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)

From Paolo P. Lava, May 14 2010: (Start)

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

a(n) = (1/2)*(3 - 2*I^n + (-1)^n - 2*(-I)^n), I = sqrt(-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: A174699 A213027 A035253 * A170989 A253004 A253011

Adjacent sequences:  A070429 A070430 A070431 * A070433 A070434 A070435

KEYWORD

nonn,easy,mult

AUTHOR

N. J. A. Sloane, May 12 2002

STATUS

approved

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Last modified March 23 20:14 EDT 2017. Contains 283957 sequences.