OFFSET
0,1
COMMENTS
The oblong numbers (A002378) not divisible by 3. - Gionata Neri, May 10 2015
The continued fraction expansion of sqrt(a(n)+1) is [3n+1; {1, 1, 2n, 1, 1,6n+2}]. For n=0, this collapses to [1; {1, 2}]. - Magus K. Chu, Nov 13 2024
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) = 2*A060544(n+1).
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 (A387235). - 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)
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)
E.g.f.: exp(x)*(2 + 18*x + 9*x^2). - Stefano Spezia, Aug 23 2025
From Elmo R. Oliveira, Sep 08 2025: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
a(n) = A144410(n)/4. (End)
MAPLE
MATHEMATICA
Table[(3*n+1)*(3*n+2), {n, 50}] (* Vladimir Joseph Stephan Orlovsky, Jan 22 2012 *)
LinearRecurrence[{3, -3, 1}, {2, 20, 56}, 80] (* Harvey P. Dale, Mar 16 2025 *)
PROG
(PARI) a(n)=(3*n+1)*(3*n+2) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved