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
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).
Programs
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Maple
A001504:=n->(3*n+1)*(3*n+2): seq(A001504(n), n=0..100); # Wesley Ivan Hurt, Jan 29 2017
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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 *) -
PARI
a(n)=(3*n+1)*(3*n+2) \\ Charles R Greathouse IV, Jun 17 2017
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 (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
Comments