OFFSET
1,2
COMMENTS
Quasipolynomial with period 3 (see formulas below).
LINKS
J. Schneider, Enumeration and Quasipolynomiality of Chip-Firing Configurations, arXiv:1104.0279 [math.CO], 2011.
Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).
FORMULA
a(3*k) = (3*k^2 + 3*k - 2)/2,
a(3*k+1) = (3*k^2 + 5*k + 2)/2,
a(3*k+2) = (3*k^2 + 7*k + 4)/2.
G.f.: x*(1 - x^2 + 2*x^3 - x^4)/((1 + x + x^2)*(1 - x)^3). [Bruno Berselli, Feb 03 2016]
a(n) = (n*(n + 3) - 4*(-1)^floor(2*n/3 + 1/3) - 2)/6. [Bruno Berselli, Feb 03 2016]
EXAMPLE
For n=4, a(4)=5 because the reachable configurations are: (4, 0, 0), (2, 1, 1), (0, 2, 2), (1, 0, 3), (3, 0, 1).
MATHEMATICA
Table[(n (n + 3) - 4 (-1)^Floor[2 n/3 + 1/3] - 2)/6, {n, 1, 80}]
(* Bruno Berselli, Feb 03 2016 *)
PROG
(Sage) [(n*(n+3)-4*(-1)^floor(2*n/3+1/3)-2)/6 for n in (1..80)] # Bruno Berselli, Feb 03 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jon Schneider, Apr 05 2011
STATUS
approved