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

0,3

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).

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

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 *)

Prog

(Magma) [Modexp(n, 2, 16 ): n in [0..100]]; // Vincenzo Librandi, Mar 28 2016
(PARI) a(n)=n^2%16 \\ Charles R Greathouse IV, Apr 06 2016

Crossrefs

Cf. A054580, A130909.

Sequence in context: A254133 A303984 A336308 * A298744 A272102 A056584

Adjacent sequences: A070436 A070437 A070438 * A070440 A070441 A070442

Keyword

nonn,easy

Author

N. J. A. Sloane, May 12 2002

Status

approved