A011886 -id:A011886 - cp's OEIS frontend

A011910 a(n) = floor( n(n-1)(n-2)/28 ).

0, 0, 0, 0, 0, 2, 4, 7, 12, 18, 25, 35, 47, 61, 78, 97, 120, 145, 174, 207, 244, 285, 330, 379, 433, 492, 557, 626, 702, 783, 870, 963, 1062, 1169, 1282, 1402, 1530, 1665, 1807, 1958, 2117, 2284, 2460, 2644, 2838, 3040, 3252, 3474, 3706, 3948, 4200, 4462, 4735, 5019, 5315, 5621, 5940, 6270, 6612, 6966, 7332, 7712, 8104, 8509, 8928, 9360, 9805, 10265, 10739, 11227

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-3,3,-1).

Cf. A011886.

[Floor((n*(n-1)*(n-2))/28): n in [0..80]]; // Vincenzo Librandi, Feb 27 2014

A011910:=n->floor(n*(n-1)*(n-2)/28); seq(A011910(n), n=0..80); # Wesley Ivan Hurt, Feb 25 2014

Table[Floor[(n(n-1)(n-2))/28],{n,0,80}] (* Harvey P. Dale, Sep 13 2011 *)

[3*binomial(n,3)//14 for n in range(81)] # G. C. Greubel, Oct 19 2024

a(n) = floor(A007531(n)/28). - Wesley Ivan Hurt, Feb 25 2014

G.f.: x^5*(2-2*x+x^2+x^3-x^4+2*x^6-x^7+x^9-x^10+2*x^11-2*x^12+2*x^13+x^19+ x^21-2*x^22+3*x^23-2*x^24+x^25)/((1-x)^4*(1+x)*(1+x^2)*(1-x+x^2-x^3+x^4-x^5+x^6)*(1+x+x^2+x^3+x^4+x^5+x^6)*(1-x^2+x^4-x^6+x^8-x^10+x^12)). - Peter J. C. Moses, Jun 02 2014

A011911 a(n) = floor( n(n-1)(n-2)/29 ).

Original entry on oeis.org

0, 0, 0, 0, 0, 2, 4, 7, 11, 17, 24, 34, 45, 59, 75, 94, 115, 140, 168, 200, 235, 275, 318, 366, 418, 475, 537, 605, 677, 756, 840, 930, 1026, 1128, 1238, 1354, 1477, 1607, 1745, 1890, 2044, 2205, 2375, 2553, 2740, 2935, 3140, 3354, 3578, 3811, 4055, 4308, 4572, 4846, 5131, 5427, 5735, 6053, 6384, 6726, 7080, 7446, 7824, 8216, 8620, 9037, 9467, 9911, 10368, 10840

Offset: 0

N. J. A. Sloane

nonn

G. C. Greubel, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-3,3,-1).

Cf. A011886.

[Floor(6*Binomial(n,3)/29): n in [0..80]]; // G. C. Greubel, Oct 19 2024

Floor[6*Binomial[Range[0,75], 3]/29] (* G. C. Greubel, Oct 19 2024 *)
Table[Floor[(2n-3n^2+n^3)/29],{n,0,100}] (* Harvey P. Dale, Jan 25 2025 *)

[6*binomial(n,3)//29 for n in range(81)] # G. C. Greubel, Oct 19 2024

G.f.: x^5*(2+x*(-2+x+x^3-x^4+2*x^5-2*x^6+2*x^7-x^8+x^9-x^10+2*x^11-x^12+x^13-x^14+2*x^15-2*x^16+2*x^17-x^18+x^19+x^21-2*x^22+3*x^23-2*x^24+x^25))/((1-x)^3*(1-x^29)). - Peter J. C. Moses, Jun 02 2014

More terms added by G. C. Greubel, Oct 19 2024

A011912 a(n) = floor(n(n-1)(n-2)/30).

Original entry on oeis.org

0, 0, 0, 0, 0, 2, 4, 7, 11, 16, 24, 33, 44, 57, 72, 91, 112, 136, 163, 193, 228, 266, 308, 354, 404, 460, 520, 585, 655, 730, 812, 899, 992, 1091, 1196, 1309, 1428, 1554, 1687, 1827, 1976, 2132, 2296, 2468, 2648, 2838, 3036, 3243, 3459, 3684, 3920, 4165, 4420, 4685, 4960, 5247, 5544, 5852, 6171, 6501, 6844, 7198, 7564, 7942, 8332, 8736, 9152, 9581, 10023, 10478, 10948

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,1,-3,3,-1).

Cf. A011886.

[Floor(n*(n-1)*(n-2)/30): n in [0..80]]; // Vincenzo Librandi, Jul 07 2012

seq(floor(binomial(n,3)/5), n=0..80); # Zerinvary Lajos, Jan 12 2009

Table[Floor[(n(n-1)(n-2))/30],{n,0,80}] (* or *) LinearRecurrence[{3,-3,1,0, 1,-3,3,-1},{0,0,0,0,0,2,4,7},81] (* Harvey P. Dale, Jun 20 2011 *)
CoefficientList[Series[x^5*(x^2-2*x+2)/((-1+x)^4*(x^4+x^3+x^2+x+1)),{x,0,80}],x] (* Vincenzo Librandi, Jul 07 2012 *)

[binomial(n,3)//5 for n in range(81)] # G. C. Greubel, Oct 19 2024

From R. J. Mathar, Apr 15 2010: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-5) - 3*a(n-6) + 3*a(n-7) - a(n-8).
G.f.: x^5*(2-2*x+x^2) / ( (1-x)^4*(1+x+x^2+x^3+x^4) ). (End)

A011913 a(n) = floor(n(n - 1)(n - 2)/31).

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 3, 6, 10, 16, 23, 31, 42, 55, 70, 88, 108, 131, 157, 187, 220, 257, 298, 342, 391, 445, 503, 566, 634, 707, 785, 870, 960, 1056, 1158, 1266, 1381, 1503, 1632, 1768, 1912, 2063, 2221, 2388, 2563, 2746, 2938, 3138, 3347, 3565, 3793, 4030, 4277, 4534, 4800, 5077, 5365, 5663, 5972, 6292, 6623, 6965, 7320, 7686, 8064, 8454, 8856, 9271, 9699, 10140, 10594

Offset: 0

N. J. A. Sloane

nonn

G. C. Greubel, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-3,3,-1).

Cf. A011886.

[Floor(6*Binomial(n,3)/31): n in [0..80]]; // G. C. Greubel, Oct 19 2024

Floor[6*Binomial[Range[0,80], 3]/31] (* G. C. Greubel, Oct 19 2024 *)

a(n) = n*(n-1)*(n-2)\31 \\ Jianing Song, Oct 15 2018

[6*binomial(n,3)//31 for n in range(81)] # G. C. Greubel, Oct 19 2024

G.f.: x^5*(1 +x^4 -x^5 +2*x^7 -x^8 +x^10 -x^11 +x^12 +x^14 -x^15 +x^16 -x^18 +2*x^19 -x^21 +x^22 +2*x^26 -2*x^27 +x^28)/((1-x)^3*(1-x^31)). - Peter J. C. Moses, Jun 02 2014

More terms added by G. C. Greubel, Oct 19 2024

A011914 a(n) = floor(n(n - 1)(n - 2)/32).

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 3, 6, 10, 15, 22, 30, 41, 53, 68, 85, 105, 127, 153, 181, 213, 249, 288, 332, 379, 431, 487, 548, 614, 685, 761, 842, 930, 1023, 1122, 1227, 1338, 1456, 1581, 1713, 1852, 1998, 2152, 2313, 2483, 2660, 2846, 3040, 3243, 3454, 3675, 3904, 4143, 4392, 4650, 4919, 5197, 5486, 5785, 6095, 6416, 6748, 7091, 7445, 7812, 8190

Offset: 0

N. J. A. Sloane, Dec 11 1996

G. C. Greubel, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-3,3,-1).

Cf. A011886.

[Floor(n*(n-1)*(n-2)/32): n in [0..80]]; // Wesley Ivan Hurt, Jun 02 2014

A011914:=n->floor(n*(n-1)*(n-2)/32); seq(A011914(n), n=0..80); # Wesley Ivan Hurt, Jun 02 2014

Table[Floor[n (n-1)(n-2)/32], {n,0,80}] (* Wesley Ivan Hurt, Jun 02 2014 *)

a(n) = n*(n-1)*(n-2)\32 \\ Jianing Song, Oct 15 2018

[3*binomial(n,3)//16 for n in range(81)] # G. C. Greubel, Oct 20 2024

G.f.: x^5*(1-x+x^2)*(1 +x -x^3 -x^4 +x^5 +x^6 +2*x^7 -x^8 -x^9 -x^10 +x^11 +x^12 +2*x^13 -x^14 -x^15 +2*x^18 -x^21 +x^23 +x^24 -x^26 +x^27)/((1-x)^4*(1 +x)*(1+x^2)*(1+x^4)*(1+x^8)*(1+x^16)). - Peter J. C. Moses, Jun 02 2014

More terms added by G. C. Greubel, Oct 20 2024

cp's OEIS Frontend

A011910 a(n) = floor( n*(n-1)*(n-2)/28 ).

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A011911 a(n) = floor( n*(n-1)*(n-2)/29 ).

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A011912 a(n) = floor(n*(n-1)*(n-2)/30).

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A011913 a(n) = floor(n*(n - 1)*(n - 2)/31).

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A011914 a(n) = floor(n*(n - 1)*(n - 2)/32).

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Magma

Maple

Mathematica

PARI

SageMath

Formula

Extensions

A011910 a(n) = floor( n(n-1)(n-2)/28 ).

A011911 a(n) = floor( n(n-1)(n-2)/29 ).

A011912 a(n) = floor(n(n-1)(n-2)/30).

A011913 a(n) = floor(n(n - 1)(n - 2)/31).

A011914 a(n) = floor(n(n - 1)(n - 2)/32).