A011907 a(n) = floor( n*(n-1)*(n-2)/25 ).
0, 0, 0, 0, 0, 2, 4, 8, 13, 20, 28, 39, 52, 68, 87, 109, 134, 163, 195, 232, 273, 319, 369, 425, 485, 552, 624, 702, 786, 876, 974, 1078, 1190, 1309, 1436, 1570, 1713, 1864, 2024, 2193, 2371, 2558, 2755, 2961, 3178, 3405, 3643, 3891, 4151, 4421, 4704, 4998, 5304, 5622, 5952, 6296, 6652, 7022, 7405, 7802, 8212, 8637, 9076, 9530, 9999, 10483, 10982, 11497, 12027
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..2000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-3,3,-1).
Crossrefs
Cf. A011886.
Programs
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Magma
[Floor(6*Binomial(n,3)/25): n in [0..75]]; // G. C. Greubel, Oct 18 2024
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Mathematica
Table[Floor[(n(n-1)(n-2))/25],{n,0,75}] (* Harvey P. Dale, Aug 25 2021 *) -
PARI
a(n)=n*(n-1)*(n-2)\25 \\ Charles R Greathouse IV, Oct 21 2022
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SageMath
[6*binomial(n,3)//25 for n in range(76)] # G. C. Greubel, Oct 18 2024
Formula
From R. J. Mathar, Apr 15 2010: (Start)
a(n) = +3*a(n-1) -3*a(n-2) +a(n-3) +a(n-25) -3*a(n-26) +3*a(n-27) -a(n-28).
G.f.: x^5*(2-2*x+2*x^2-x^3+x^4-x^5+2*x^6-x^7+x^8+x^12-x^13+2*x^14-x^15+x^16-x^17+2*x^18-2*x^19+3*x^20-2*x^21+x^22) / ( (1-x)^4*(1+x^4+x^3+x^2+x)*(1+x^5+x^10+x^15+x^20) ). (End)
Extensions
More terms added by G. C. Greubel, Oct 18 2024