A011891 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A011891

a(n) = floor( n*(n-1)*(n-2)/9 ).

0, 0, 0, 0, 2, 6, 13, 23, 37, 56, 80, 110, 146, 190, 242, 303, 373, 453, 544, 646, 760, 886, 1026, 1180, 1349, 1533, 1733, 1950, 2184, 2436, 2706, 2996, 3306, 3637, 3989, 4363, 4760, 5180, 5624, 6092, 6586, 7106, 7653, 8227, 8829, 9460, 10120, 10810, 11530

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,5

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Index entries for linear recurrences with constant coefficients, signature (4,-6,3,3,-6,3,3,-6,4,-1).

FORMULA

G.f.: x^4*(2-2*x+x^2+x^3-x^4+x^5)/((1+x^3+x^6)*(1-x)^4). [Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009]

Third differences are [-2, 4] repeated. - M. F. Hasler, Sep 15 2009

MATHEMATICA

Table[Floor[(n(n-1)(n-2))/9], {n, 0, 40}] (* or *)

LinearRecurrence[{4, -6, 3, 3, -6, 3, 3, -6, 4, -1}, {0, 0, 0, 0, 2, 6, 13, 23, 37, 56}, 50] (* Harvey P. Dale, Feb 20 2017 *)

PROG

(Magma) [Floor(n*(n-1)*(n-2)/9): n in [0..50]]; // Vincenzo Librandi, Feb 23 2017

(SageMath) [2*binomial(n, 3)//3 for n in range(51)] # G. C. Greubel, Oct 06 2024

CROSSREFS

Cf. A011886.

Sequence in context: A293503 A143689 A180773 * A370880 A184533 A338991

Adjacent sequences: A011888 A011889 A011890 * A011892 A011893 A011894

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved