A001504 a(n) = (3*n+1)*(3*n+2).

2, 20, 56, 110, 182, 272, 380, 506, 650, 812, 992, 1190, 1406, 1640, 1892, 2162, 2450, 2756, 3080, 3422, 3782, 4160, 4556, 4970, 5402, 5852, 6320, 6806, 7310, 7832, 8372, 8930, 9506, 10100, 10712, 11342, 11990, 12656, 13340, 14042, 14762, 15500, 16256, 17030

Offset

0,1

Comments

The oblong numbers (A002378) not divisible by 3. - Gionata Neri, May 10 2015

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = A060544(n+1)*2.

Sum_{k>=0} 1/a(k) = (Pi/3)/sqrt(3) = A073010. - Benoit Cloitre, Aug 20 2002

a(n) = 18*n + a(n-1) with a(0) = 2. - Vincenzo Librandi, Nov 12 2010

Sum_{n>=0} (-1)^n/a(n) = 2*log(2)/3. - Amiram Eldar, Jan 14 2021

G.f.: -2*(x^2+7*x+1)/(x-1)^3. - Alois P. Heinz, Feb 28 2021

From Amiram Eldar, Feb 19 2023: (Start)

a(n) = A016777(n)*A016789(n).

Product_{n>=0} (1 - 1/a(n)) = 2*cos(sqrt(5)*Pi/6)/sqrt(3).

Product_{n>=0} (1 + 1/a(n)) = 2*cosh(sqrt(3)*Pi/6)/sqrt(3). (End)

Maple

A001504:=n->(3*n+1)*(3*n+2): seq(A001504(n), n=0..100); # Wesley Ivan Hurt, Jan 29 2017

Mathematica

Table[(3*n+1)*(3*n+2), {n, 50}] (* Vladimir Joseph Stephan Orlovsky, Jan 22 2012 *)

Prog

(PARI) a(n)=(3*n+1)*(3*n+2) \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Subsequence of A002378.

Cf. A016777, A016789, A060544, A073010.

Sequence in context: A331090 A139271 A133217 * A192351 A136905 A230644

Adjacent sequences: A001501 A001502 A001503 * A001505 A001506 A001507

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved