A228887 a(n) = binomial(3*n + 1,3).

4, 35, 120, 286, 560, 969, 1540, 2300, 3276, 4495, 5984, 7770, 9880, 12341, 15180, 18424, 22100, 26235, 30856, 35990, 41664, 47905, 54740, 62196, 70300, 79079, 88560, 98770, 109736, 121485, 134044, 147440, 161700, 176851, 192920, 209934, 227920, 246905

Offset: 1

Author

Peter Bala, Sep 09 2013

Keywords

• nonn
• easy

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. A006566 (binomial(3*n,3)) and A228888 (binomial(3*n + 2,3)).

Programs

Magma

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

Maple

seq(binomial(3*n+1,3), n = 1..38);

Mathematica

Table[(Binomial[3n + 1, 3]), {n, 40}] (* Vincenzo Librandi, Sep 10 2013 *)
LinearRecurrence[{4,-6,4,-1},{4,35,120,286},40] (* Harvey P. Dale, Jan 11 2015 *)

Formula

a(n) = -a(-n) = binomial(3*n + 1,3) = 1/6*(3*n + 1)*(3*n)*(3*n - 1).

G.f.: x*(4 + 19*x + 4*x^2)/(1 - x)^4 = 4*x + 35*x^2 + 120*x^3 + ....

Sum_{n>=1} 1/a(n) = 3*log(3) - 3.

Sum_{n>=1} (-1)^n/a(n) = 4*log(2) - 3.

E.g.f.: exp(x)*x*(8 + 27*x + 9*x^2)/2. - Stefano Spezia, Sep 20 2024