A011896 a(n) = floor( n*(n-1)*(n-2)/14 ).

0, 0, 0, 0, 1, 4, 8, 15, 24, 36, 51, 70, 94, 122, 156, 195, 240, 291, 349, 415, 488, 570, 660, 759, 867, 985, 1114, 1253, 1404, 1566, 1740, 1926, 2125, 2338, 2564, 2805, 3060, 3330, 3615, 3916, 4234, 4568, 4920, 5289, 5676, 6081, 6505, 6949, 7412, 7896

Offset

0,6

Links

G. C. Greubel, Table of n, a(n) for n = 0..2000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,0,1,-3,3,-1).

Formula

G.f.: x^4*(1+x-x^2+2*x^3-x^4+x^5)/((1-x)^3*(1-x^7)).

a(2-n) = (-1)*A055610(n).

Mathematica

Table[Floor[(n(n-1)(n-2))/14], {n, 0, 50}] (* or  *)
LinearRecurrence[{3, -3, 1, 0, 0, 0, 1, -3, 3, -1}, {0, 0, 0, 0, 1, 4, 8, 15, 24, 36}, 50] (* Harvey P. Dale, Jan 03 2024 *)

Prog

(PARI) a(n)=n*(n-1)*(n-2)\14
(Magma) [Floor(3*Binomial(n, 3)/7): n in [0..50]]; // G. C. Greubel, Oct 16 2024
(SageMath) [3*binomial(n, 3)//7 for n in range(51)] # G. C. Greubel, Oct 16 2024

Crossrefs

Cf. A011886, A055610.

Sequence in context: A213035 A014146 A049845 * A333266 A024624 A350162

Adjacent sequences: A011893 A011894 A011895 * A011897 A011898 A011899

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Additional comments from Michael Somos, Jun 02 2000.

Status

approved