A228889 a(n) = 3*n*(3*n + 1)*(3*n + 2).

60, 336, 990, 2184, 4080, 6840, 10626, 15600, 21924, 29760, 39270, 50616, 63960, 79464, 97290, 117600, 140556, 166320, 195054, 226920, 262080, 300696, 342930, 388944, 438900, 492960, 551286, 614040, 681384, 753480, 830490, 912576, 999900, 1092624, 1190910

Offset: 1

Author

Peter Bala, Sep 09 2013

Keywords

• nonn
• easy

Comments

Related sequences are A054776 and A097321.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A054776, A097321, A228888.

Programs

Magma

[3*n*(3*n+1)*(3*n+2): n in [1..40]]; // Vincenzo Librandi, Sep 10 2013

Maple

seq(3*n*(3*n+1)*(3*n+2), n = 1..35);

Mathematica

CoefficientList[Series[6 (10 + 16 x + x^2)/(1 - x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Sep 10 2013 *)
Table[Times@@(3n+{0,1,2}),{n,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{60,336,990,2184},40] (* Harvey P. Dale, Dec 20 2023 *)

Formula

a(n) = 3*n*(3*n + 1)*(3*n + 2) = 6*binomial(3*n + 2,3) = 6*A228888(n).

a(-n) = - A054776(n).

G.f.: 6*x*(10 + 16*x + x^2)/(1 - x)^4 = 60*x + 336*x^2 + 990*x^3 + ....

Sum {n >= 1} 1/a(n) = 3/4 - log(3)/4 - 1/12*sqrt(3)*Pi;

Sum {n >= 1} (-1)^n/a(n) = 3/4 - 2/3*log(2) - 1/18*sqrt(3)*Pi.