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A070432 Period 4: repeat [0, 1, 4, 1]; a(n) = n^2 mod 8. 7

%I

%S 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,

%T 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,

%U 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

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

%C Multiplicative with a(2) = 4, a(2^e) = 0 if e >= 2, a(p^e) = 1 otherwise. - _David W. Wilson_, Jun 12 2005

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1). - _R. J. Mathar_, Apr 20 2010

%F From _R. J. Mathar_, Apr 20 2010: (Start)

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

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

%F From _Paolo P. Lava_, May 14 2010: (Start)

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

%F a(n) = (1/2)*(3 - 2*I^n + (-1)^n - 2*(-I)^n), I = sqrt(-1). (End)

%F Dirichlet g.f.: zeta(s)*(1 + 4*2^(-s))*(1 - 2^(-s)). - _R. J. Mathar_, Mar 10 2011

%F a(n) = (n mod 2) + 4*floor(((n+1) mod 4)/3). - _Gary Detlefs_, Dec 29 2011

%F From _Wesley Ivan Hurt_, Mar 19 2015: (Start)

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

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

%F E.g.f.: 2*cosh(x) + sinh(x) - 2*cos(x). - _G. C. Greubel_, Mar 22 2016

%F a(n) = (3 + cos(n*Pi) - 4*cos(n*Pi/2))/2. - _Wesley Ivan Hurt_, Dec 21 2016

%F a(n) = a(-n) for all n in Z. - _Michael Somos_, Dec 22 2016

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

%p seq(n mod 2 + 4*floor(((n+1) mod 4)/3), n = 0..200) # _Gary Detlefs_, Dec 29 2011

%t Table[Mod[n^2, 8], {n, 0, 99}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 21 2011 *)

%t Mod[Range[0, 99]^2, 8] (* _Alonso del Arte_, Mar 20 2015 *)

%o (PARI) a(n)=n^2%8 \\ _Charles R Greathouse IV_, Oct 07 2015

%o (MAGMA) &cat [[0, 1, 4, 1]^^30]; // _Wesley Ivan Hurt_, Dec 21 2016

%Y Cf. A070430, A070431.

%K nonn,easy,mult

%O 0,3

%A _N. J. A. Sloane_, May 12 2002

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Last modified January 17 23:15 EST 2019. Contains 319251 sequences. (Running on oeis4.)