A070439 a(n) = n^2 mod 16.

0, 1, 4, 9, 0, 9, 4, 1, 0, 1, 4, 9, 0, 9, 4, 1, 0, 1, 4, 9, 0, 9, 4, 1, 0, 1, 4, 9, 0, 9, 4, 1, 0, 1, 4, 9, 0, 9, 4, 1, 0, 1, 4, 9, 0, 9, 4, 1, 0, 1, 4, 9, 0, 9, 4, 1, 0, 1, 4, 9, 0, 9, 4, 1, 0, 1, 4, 9, 0, 9, 4, 1, 0, 1, 4, 9, 0, 9, 4, 1, 0, 1, 4, 9, 0, 9, 4, 1, 0, 1, 4, 9, 0, 9, 4, 1, 0, 1, 4, 9, 0

Offset: 0

Author

N. J. A. Sloane, May 12 2002

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1).

Crossrefs

Cf. A054580, A130909.

Programs

Magma

[Modexp(n, 2, 16 ): n in [0..100]]; // Vincenzo Librandi, Mar 28 2016

Mathematica

Table[Mod[n^2,16],{n,0,200}] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2011 *)
CoefficientList[Series[(x + 4 x^2 + 9 x^3 + 9 x^5 + 4 x^6 + x^7) / (1 - x^8), {x, 0, 100}], x] (* Vincenzo Librandi, Mar 25 2016 *)
PowerMod[Range[0,100],2,16] (* Harvey P. Dale, Jul 23 2023 *)

PARI

a(n)=n^2%16 \\ Charles R Greathouse IV, Apr 06 2016

Formula

G.f.: -x*(1+4*x+9*x^2+9*x^4+4*x^5+x^6) / ( (x-1)*(1+x)*(x^2+1)*(x^4+1) ). - R. J. Mathar, Jul 27 2015

a(n) = a(n-8). - G. C. Greubel, Mar 24 2016

a(n) = A130909(n^2). - Michel Marcus, Mar 24 2016