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A011901
a(n) = floor( n*(n-1)*(n-2)/19 ).
2
0, 0, 0, 0, 1, 3, 6, 11, 17, 26, 37, 52, 69, 90, 114, 143, 176, 214, 257, 306, 360, 420, 486, 559, 639, 726, 821, 923, 1034, 1153, 1282, 1419, 1566, 1722, 1889, 2066, 2254, 2453, 2664, 2886, 3120, 3366, 3625, 3897, 4182, 4481, 4793, 5120, 5461, 5818, 6189, 6576, 6978, 7397, 7832, 8284, 8753, 9240, 9744, 10266, 10806, 11365, 11943, 12540, 13157, 13793, 14450, 15127
OFFSET
0,6
LINKS
Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-3,3,-1).
FORMULA
a(n) = +3*a(n-1) -3*a(n-2) +a(n-3) +a(n-19) -3*a(n-20) +3*a(n-21) -a(n-22). - R. J. Mathar, Apr 15 2010
G.f.: x^4 (1+x^4) (1+x^3 (1-x+x^3+x^6) (1+(-1+x) x (1+x^2)))/(1+x (-3+x (3+x (-1+(-1+x)^3 x^16)))). - Peter J. C. Moses, Jun 02 2014
G.f.: x^4*(1+x^4)*(1+x^3-2*x^4+2*x^5-x^6+x^7+x^11-x^12+x^13)/((1-x)^3*(1-x^19)). - G. C. Greubel, Oct 17 2024
MATHEMATICA
Table[Floor[n(n-1)(n-2)/19], {n, 0, 75}] (* or *)
LinearRecurrence[{3, -3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -3, 3, -1}, {0, 0, 0, 0, 1, 3, 6, 11, 17, 26, 37, 52, 69, 90, 114, 143, 176, 214, 257, 306, 360, 420}, 76] (* Harvey P. Dale, May 30 2021 *)
PROG
(PARI) a(n)=n*(n-1)*(n-2)\19 \\ Charles R Greathouse IV, Oct 21 2022
(Magma) [Floor(6*Binomial(n, 3)/19): n in [0..75]]; // G. C. Greubel, Oct 17 2024
(SageMath)_[6*binomial(n, 3)//19 for n in range(76)] # G. C. Greubel, Oct 17 2024
CROSSREFS
Cf. A011886.
Sequence in context: A107957 A000603 A003453 * A169739 A109471 A279032
KEYWORD
nonn,easy
EXTENSIONS
More terms added by G. C. Greubel, Oct 18 2024
STATUS
approved