OFFSET
0,3
COMMENTS
Decimal expansion of 208284810/1111111111. - Alexander R. Povolotsky, Mar 08 2013
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,1).
FORMULA
Periodic with period 10. - Franklin T. Adams-Watters, Mar 13 2006
a(n) = 4.5 -cos(Pi*n/5) +(1/2*(-(5-5^(1/2))^(1/2) +(5+5^(1/2))^(1/2))*2^(1/2))*sin(Pi*n/5) -cos(2*Pi*n/5) +(-1/10*(-(5-5^(1/2))^(1/2)+3*(5+5^(1/2))^(1/2))*2^(1/2))*sin(2*Pi*n/5) -cos(3*Pi*n/5) +(-1/2*((5-5^(1/2))^(1/2) +(5+5^(1/2))^(1/2))*2^(1/2))*sin(3*Pi*n/5) -cos(4*Pi*n/5) +( -1/10*(3*(5-5^(1/2))^(1/2) +(5 +5^(1/2))^(1/2))*2^(1/2))*sin(4*Pi*n/5) -0.5*(-1)^n. - Richard Choulet, Dec 12 2008
a(n) = n^k mod 10; for k > 0 where k mod 4 = 3. - Doug Bell, Jun 15 2015
G.f.: x*(1+8*x+7*x^2+4*x^3+5*x^4+6*x^5+3*x^6+2*x^7+9*x^8) / ((1-x)*(1+x)*(1-x+x^2-x^3+x^4)*(1+x+x^2+x^3+x^4)). - Colin Barker, Nov 30 2015
MATHEMATICA
Table[Mod[n^3, 10], {n, 0, 200}] (* Vladimir Joseph Stephan Orlovsky, Apr 23 2011 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 1, 8, 7, 4, 5, 6, 3, 2, 9}, 81] (* Ray Chandler, Aug 26 2015 *)
PROG
(Sage) [power_mod(n, 3, 10 ) for n in range(0, 81)] # Zerinvary Lajos, Oct 29 2009
(PARI) a(n)=n^3%10 \\ Charles R Greathouse IV, Mar 08 2013
(Magma) [n^3 mod 10: n in [0..80]]; // Vincenzo Librandi, Mar 26 2013
(PARI) concat(0, Vec(x*(1+8*x+7*x^2+4*x^3+5*x^4+6*x^5+3*x^6+2*x^7+9*x^8) / ((1-x)*(1+x)*(1-x+x^2-x^3+x^4)*(1+x+x^2+x^3+x^4)) + O(x^100))) \\ Colin Barker, Nov 30 2015
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
STATUS
approved