OFFSET
0,5
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1,1,-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-4) -3*a(n-5) +3*a(n-6) -a(n-7).
G.f.: x^3*(1+3*x+2*x^3) / ( (1-x)^4*(1+x)*(1+x^2) ). (End)
a(n) = floor(Sum_{k=0..n} n*(k+1)/2) for n >= -2. - William A. Tedeschi, Sep 10 2010
MATHEMATICA
Table[Floor[(n(n-1)(n-2))/4], {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1, 1, -3, 3, -1}, {0, 0, 0, 1, 6, 15, 30}, 50] (* Harvey P. Dale, Feb 25 2012 *)
CoefficientList[Series[x^3*(1+3*x+2*x^3)/((1-x)^3*(1-x^4)), {x, 0, 50}], x] (* Vincenzo Librandi, Jul 07 2012 *)
PROG
(Magma) [Floor(n*(n-1)*(n-2)/4): n in [0..50]]; // Vincenzo Librandi, Jul 07 2012
(SageMath) [3*binomial(n, 3)//2 for n in range(51)] # G. C. Greubel, Oct 06 2024
CROSSREFS
Sequences of the form floor(n*(n-1)*(n-2)/m): A007531 (m=1), A135503 (m=2), A007290 (m=3), this sequence (m=4), A011887 (m=5), A000292 (m=6), A011889 (m=7), A011890 (m=8), A011891 (m=9), A011892 (m=10), A011893 (m=11), A011894 (m=12), A011895 (m=13), A011896 (m=14), A011897 (m=15), A011898 (m=16), A011899 (m=17), A011849 (m=18), A011901 (m=19), A011902 (m=20), A011903 (m=21), A011904 (m=22), A011905 (m=23), A011842 (m=24), A011907 (m=25), A011908 (m=26), A011909 (m=27), A011910 (m=28), A011911 (m=29), A011912 (m=30), A011912 (m=31), A011913 (m=32).
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from William A. Tedeschi, Sep 10 2010
STATUS
approved