A213032 a(n) = floor(n/2)*floor(n/3)-floor(n/6)^2.

0, 0, 0, 1, 2, 2, 5, 5, 7, 11, 14, 14, 20, 20, 24, 31, 36, 36, 45, 45, 51, 61, 68, 68, 80, 80, 88, 101, 110, 110, 125, 125, 135, 151, 162, 162, 180, 180, 192, 211, 224, 224, 245, 245, 259, 281, 296, 296, 320, 320, 336, 361, 378, 378, 405, 405, 423, 451

Offset: 0

Author

Clark Kimberling, Jun 05 2012

Keywords

• nonn
• easy

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).

Programs

Magma

[Floor(n/2)*Floor(n/3)-Floor(n/6)^2: n in [0..80]]; // Vincenzo Librandi, Aug 02 2013

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 *)

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).