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A011896
a(n) = floor( n*(n-1)*(n-2)/14 ).
3
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
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
Sequence in context: A213035 A014146 A049845 * A333266 A024624 A350162
KEYWORD
nonn
EXTENSIONS
Additional comments from Michael Somos, Jun 02 2000.
STATUS
approved