OFFSET
0,6
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,1,-3,3,-1).
FORMULA
From R. J. Mathar, Apr 15 2010: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-5) - 3*a(n-6) + 3*a(n-7) - a(n-8).
G.f.: x^5*(2-2*x+x^2) / ( (1-x)^4*(1+x+x^2+x^3+x^4) ). (End)
MAPLE
seq(floor(binomial(n, 3)/5), n=0..80); # Zerinvary Lajos, Jan 12 2009
MATHEMATICA
Table[Floor[(n(n-1)(n-2))/30], {n, 0, 80}] (* or *) LinearRecurrence[{3, -3, 1, 0, 1, -3, 3, -1}, {0, 0, 0, 0, 0, 2, 4, 7}, 81] (* Harvey P. Dale, Jun 20 2011 *)
CoefficientList[Series[x^5*(x^2-2*x+2)/((-1+x)^4*(x^4+x^3+x^2+x+1)), {x, 0, 80}], x] (* Vincenzo Librandi, Jul 07 2012 *)
PROG
(Magma) [Floor(n*(n-1)*(n-2)/30): n in [0..80]]; // Vincenzo Librandi, Jul 07 2012
(SageMath) [binomial(n, 3)//5 for n in range(81)] # G. C. Greubel, Oct 19 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved