OFFSET
0,2
COMMENTS
Number of distinct n-digit suffixes of base 5 squares.
REFERENCES
J. V. Uspensky and M. A. Heaslet, Elementary Number Theory, McGraw-Hill, NY, 1939, p. 324.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,1,-5).
FORMULA
a(n) = floor((5^n+3)*5/12).
G.f.: (1-2*x-5*x^2)/((1-x)*(1+x)*(1-5*x)). [Colin Barker, Mar 14 2012]
a(n) = 5*a(n-1) +a(n-2) -5*a(n-3). Vincenzo Librandi, Apr 21 2012
a(n) = A000224(5^n). - R. J. Mathar, Sep 28 2017
MAPLE
A039302 := proc(n)
floor((5^n+3)*5/12) ;
end proc:
seq(A039302(n), n=0..10) ; # R. J. Mathar, Sep 28 2017
MATHEMATICA
CoefficientList[Series[(1-2*x-5*x^2)/((1-x)*(1+x)*(1-5*x)), {x, 0, 30}], x] (* or *)LinearRecurrence[{5, 1, -5}, {1, 3, 11}, 30] (* Vincenzo Librandi, Apr 21 2012 *)
PROG
(Magma) I:=[1, 3, 11]; [n le 3 select I[n] else 5*Self(n-1)+Self(n-2)-5*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Apr 21 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved