This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A001504 #87 Aug 23 2025 09:57:22
%S A001504 2,20,56,110,182,272,380,506,650,812,992,1190,1406,1640,1892,2162,
%T A001504 2450,2756,3080,3422,3782,4160,4556,4970,5402,5852,6320,6806,7310,
%U A001504 7832,8372,8930,9506,10100,10712,11342,11990,12656,13340,14042,14762,15500,16256,17030
%N A001504 a(n) = (3*n+1)*(3*n+2).
%C A001504 The oblong numbers (A002378) not divisible by 3. - _Gionata Neri_, May 10 2015
%C A001504 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
%H A001504 T. D. Noe, <a href="/A001504/b001504.txt">Table of n, a(n) for n = 0..1000</a>
%H A001504 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A001504 a(n) = A060544(n+1)*2.
%F A001504 Sum_{k>=0} 1/a(k) = (Pi/3)/sqrt(3) = A073010. - _Benoit Cloitre_, Aug 20 2002
%F A001504 a(n) = 18*n + a(n-1) with a(0) = 2. - _Vincenzo Librandi_, Nov 12 2010
%F A001504 Sum_{n>=0} (-1)^n/a(n) = 2*log(2)/3 (A387235). - _Amiram Eldar_, Jan 14 2021
%F A001504 G.f.: -2*(x^2+7*x+1)/(x-1)^3. - _Alois P. Heinz_, Feb 28 2021
%F A001504 From _Amiram Eldar_, Feb 19 2023: (Start)
%F A001504 a(n) = A016777(n)*A016789(n).
%F A001504 Product_{n>=0} (1 - 1/a(n)) = 2*cos(sqrt(5)*Pi/6)/sqrt(3).
%F A001504 Product_{n>=0} (1 + 1/a(n)) = 2*cosh(sqrt(3)*Pi/6)/sqrt(3). (End)
%F A001504 E.g.f.: exp(x)*(2 + 18*x + 9*x^2). - _Stefano Spezia_, Aug 23 2025
%p A001504 A001504:=n->(3*n+1)*(3*n+2): seq(A001504(n), n=0..100); # _Wesley Ivan Hurt_, Jan 29 2017
%t A001504 Table[(3*n+1)*(3*n+2),{n,50}] (* _Vladimir Joseph Stephan Orlovsky_, Jan 22 2012 *)
%t A001504 LinearRecurrence[{3,-3,1},{2,20,56},80] (* _Harvey P. Dale_, Mar 16 2025 *)
%o A001504 (PARI) a(n)=(3*n+1)*(3*n+2) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A001504 Subsequence of A002378.
%Y A001504 Cf. A016777, A016789, A060544, A073010, A387235.
%K A001504 nonn,easy,changed
%O A001504 0,1
%A A001504 _N. J. A. Sloane_