OFFSET
0,3
COMMENTS
Equivalently, n^6 mod 15. - Ray Chandler, Dec 27 2023
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).
FORMULA
From Reinhard Zumkeller, Apr 24 2009: (Start)
a(m*n) = a(m)*a(n) mod 15.
a(15*n+7+k) = a(15*n+8-k) for k <= 15*n+7.
a(15*n+k) = a(15*n-k) for k <= 15*n.
a(n+15) = a(n). (End)
From R. J. Mathar, Mar 14 2011: (Start)
a(n) = a(n-15).
G.f.: -x*(1+x) *(x^12+3*x^11+6*x^10-5*x^9+15*x^8-9*x^7+13*x^6-9*x^5+15*x^4-5*x^3+6*x^2+3*x+1) / ( (x-1) *(1+x^4+x^3+x^2+x) *(1+x+x^2) *(1-x+x^3-x^4+x^5-x^7+x^8) ). (End)
G.f.: (x^14 +4*x^13 +9*x^12 +x^11 +10*x^10 +6*x^9 +4*x^8 +4*x^7 +6*x^6 +10*x^5 +x^4 +9*x^3 +4*x^2 +x)/(-x^15 +1). - Colin Barker, Aug 14 2012
MATHEMATICA
Table[Mod[n^2, 15], {n, 0, 200}] (* Vladimir Joseph Stephan Orlovsky, Apr 21 2011 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1}, 97] (* Ray Chandler, Aug 26 2015 *)
PROG
(Sage) [power_mod(n, 2, 15)for n in range(0, 97)] # Zerinvary Lajos, Nov 06 2009
(PARI) a(n)=n^2%15 \\ Charles R Greathouse IV, Sep 28 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 12 2002
STATUS
approved