A213033 - OEIS

%I #13 Jul 25 2015 10:37:42

%S 0,0,0,3,8,10,36,42,64,108,150,165,288,312,392,525,640,680,972,1026,

%T 1200,1470,1694,1771,2304,2400,2704,3159,3528,3654,4500,4650,5120,

%U 5808,6358,6545,7776,7992,8664,9633,10400,10660,12348,12642,13552

%N n*[n/2]*[n/3], where [] = floor.

%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1, 1, 0, -1, 2, 0, -2, -2, 0, 2, -1, 0, 1, 1, 0, -1).

%F a(n) = a(n-2)+a(n-3)-a(n-5)+2*a(n-6)-2*a(n-8)+2*a(n-11)-a(n-12)+a(n-14)+a(n-15)-a(n-17).

%F G.f.: (3*x^3 + 8*x^4 + 7*x^5 + 25*x^6 + 24*x^7 + 21*x^8 + 32*x^9 + 38*x^10 + 15*x^11 + 22*x^12 + 13*x^13 + 5*x^14 + 2*x^15 + x^16)/(1 - x^2 - x^3 + x^5 - 2*x^6 + 2*x^8 + 2*x^9 - 2*x^11 + x^12 - x^14 - x^15 + x^17).

%t a[n_] := n*Floor[n/2]*Floor[n/3]

%t Table[a[n], {n, 0, 90}]    (* A213033 *)

%t LinearRecurrence[{0, 1, 1, 0, -1, 2, 0, -2, -2, 0, 2, -1, 0, 1, 1, 0, -1}, {0, 0, 0, 3, 8, 10, 36, 42, 64, 108, 150, 165, 288, 312, 392, 525, 640}, 60]

%Y Cf. A242669.

%K nonn,easy

%O 0,4

%A _Clark Kimberling_, Jun 05 2012