OFFSET
0,5
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,2,-2,0,0,0,0,-1,1).
FORMULA
a(n) = a(n-1)+2*a(n-6)-2*a(n-7)-a(n-12)+a(n-13).
G.f.: (x^3 + x^4 + 3*x^6 + 2*x^8 + 2*x^9 + x^10)/(1 - x - 2*x^6 + 2*x^7 + x^12 - x^13).
MATHEMATICA
a[n_] := Floor[n/2]*Floor[n/3] - Floor[n/6]^2
Table[a[n], {n, 0, 90}] (* A213032 *)
LinearRecurrence[{1, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, -1, 1}, {0, 0, 0, 1, 2, 2, 5, 5, 7, 11, 14, 14, 20}, 90]
CoefficientList[Series[(x^3 + x^4 + 3 x^6 + 2 x^8 + 2 x^9 + x^10) / (1 - x - 2 x^6 + 2 x^7 + x^12 - x^13), {x, 0, 80}], x] (* Vincenzo Librandi, Aug 02 2013 *)
PROG
(Magma) [Floor(n/2)*Floor(n/3)-Floor(n/6)^2: n in [0..80]]; // Vincenzo Librandi, Aug 02 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 05 2012
STATUS
approved