A213033 n*[n/2]*[n/3], where [] = floor.

0, 0, 0, 3, 8, 10, 36, 42, 64, 108, 150, 165, 288, 312, 392, 525, 640, 680, 972, 1026, 1200, 1470, 1694, 1771, 2304, 2400, 2704, 3159, 3528, 3654, 4500, 4650, 5120, 5808, 6358, 6545, 7776, 7992, 8664, 9633, 10400, 10660, 12348, 12642, 13552

Offset

0,4

Links

Table of n, a(n) for n=0..44.

Index entries for linear recurrences with constant coefficients, signature (0, 1, 1, 0, -1, 2, 0, -2, -2, 0, 2, -1, 0, 1, 1, 0, -1).

Formula

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).

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).

Mathematica

a[n_] := n*Floor[n/2]*Floor[n/3]
Table[a[n], {n, 0, 90}]    (* A213033 *)
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]

Crossrefs

Cf. A242669.

Sequence in context: A332976 A032914 A088072 * A305176 A046545 A279585

Adjacent sequences: A213030 A213031 A213032 * A213034 A213035 A213036

Keyword

nonn,easy

Author

Clark Kimberling, Jun 05 2012

Status

approved