OFFSET
1,4
COMMENTS
The terms for n>1 can also be defined by: a(n)=0 if n==0 (mod 3), and otherwise a(n) equals the inverse of 3 in Z/nZ*. - José María Grau Ribas, Jun 18 2013
The subsequence of nonzero terms is essentially the same as A026741. - Giovanni Resta, Jun 18 2013
REFERENCES
F. Smarandache, Back and Forth Summants, Arizona State Univ., Special Collections, 1972.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
J. Dezert, editor, Smarandacheials, Mathematics Magazine, Aurora, Canada
Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).
FORMULA
a(3n) = 0; a(3n+1) = 2n+1; a(3n+2) = n+1.
G.f.: x*(1+x+x^3) / ( (x-1)^2*(1+x+x^2)^2 ). - R. J. Mathar, Jun 26 2013
a(n) = Sum_{k=1..n} k*( floor((3k-1)/n)-floor((3k-2)/n) ). - Anthony Browne, May 17 2016
MAPLE
f:= proc(n) local t;
t:= n mod 3;
if t = 0 then 0 elif t = 1 then 2/3*(n+1/2) else (n+1)/3 fi
end proc:
map(f, [$1..100]); # Robert Israel, May 19 2016
MATHEMATICA
LinearRecurrence[{0, 0, 2, 0, 0, -1}, {1, 1, 0, 3, 2, 0}, 100] (* Jean-François Alcover, Jun 04 2020 *)
PROG
(PARI) S(n, k=3) = local(s, x); s = n; x = n - k; while (x >= -n, s = s + x; x = x - k); s;
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jahan Tuten (jahant(AT)indiainfo.com), Mar 29 2004
EXTENSIONS
Edited and extended by David Wasserman, Dec 19 2005
STATUS
approved