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

1,1

Comments

From John King, Apr 04 2019: (Start)

In a matchstick-built Star of David, this sequence with a leading 0 is the number of triangles larger than size 1 in one orientation; there is an equal number of 'inverted' triangles.

For such a star, A045946 gives the number of matches; A135453 gives the number of size=1 triangles and A299965 gives the total number of triangles. For the triangle analogs see A045943; for the hexagon analogs see A045949. (End)

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).

Formula

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

G.f.: (4*x + 19*x^2 + 4*x^3)/(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.

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 *)

Prog

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

Crossrefs

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

Sequence in context: A257600 A211612 A068968 * A185592 A296280 A011195

Adjacent sequences: A228884 A228885 A228886 * A228888 A228889 A228890

Keyword

nonn,easy

Author

Peter Bala, Sep 09 2013

Status

approved