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A011909
a(n) = floor( n*(n-1)*(n-2)/27 ).
2
0, 0, 0, 0, 0, 2, 4, 7, 12, 18, 26, 36, 48, 63, 80, 101, 124, 151, 181, 215, 253, 295, 342, 393, 449, 511, 577, 650, 728, 812, 902, 998, 1102, 1212, 1329, 1454, 1586, 1726, 1874, 2030, 2195, 2368, 2551, 2742, 2943, 3153, 3373, 3603, 3843, 4094, 4355, 4627, 4911, 5205, 5512, 5830, 6160, 6502, 6856, 7224, 7604, 7997, 8404, 8824, 9258, 9706, 10168, 10645, 11136
OFFSET
0,6
LINKS
Index entries for linear recurrences with constant coefficients, signature (4,-6,3,3,-6,3,3,-6,3,3,-6,3,3,-6,3,3,-6,3,3,-6,3,3,-6,3,3,-6,4,-1).
FORMULA
G.f.: x^5*(1-x+x^2)*(2-2*x-x^2+3*x^3-2*x^4+3*x^6-3*x^7+2*x^9-x^10-x^11 +3*x^12-2*x^13-x^14+3*x^15-2*x^16+2*x^18-2*x^19+x^20)/((1-x)^4*(1+x^3+x^6)*(1+x^9+x^18)). - Peter J. C. Moses, Jun 02 2014
MATHEMATICA
Table[Floor[n(n-1)(n-2)/27], {n, 0, 80}] (* or *)
LinearRecurrence[{4, -6, 3, 3, -6, 3, 3, -6, 3, 3, -6, 3, 3, -6, 3, 3, -6, 3, 3, -6, 3, 3, -6, 3, 3, -6, 4, -1}, {0, 0, 0, 0, 0, 2, 4, 7, 12, 18, 26, 36, 48, 63, 80, 101, 124, 151, 181, 215, 253, 295, 342, 393, 449, 511, 577, 650}, 81] (* Harvey P. Dale, Jun 12 2023 *)
PROG
(Magma) [Floor(2*Binomial(n, 3)/9): n in [0..80]]; // G. C. Greubel, Oct 19 2024
(SageMath) [2*binomial(n, 3)//9 for n in range(81)] # G. C. Greubel, Oct 19 2024
CROSSREFS
Cf. A011886.
Sequence in context: A005521 A135901 A124197 * A065962 A173722 A049703
KEYWORD
nonn
EXTENSIONS
More terms added by G. C. Greubel, Oct 19 2024
STATUS
approved