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 A139609 #28 Apr 16 2024 10:26:09
%S A139609 9,45,81,117,153,189,225,261,297,333,369,405,441,477,513,549,585,621,
%T A139609 657,693,729,765,801,837,873,909,945,981,1017,1053,1089,1125,1161,
%U A139609 1197,1233,1269,1305,1341,1377,1413,1449,1485,1521,1557,1593,1629,1665,1701
%N A139609 a(n) = 36*n + 9.
%C A139609 Numbers of the 9th column of positive numbers in the square array of nonnegative and polygonal numbers A139600.
%H A139609 Vincenzo Librandi, <a href="/A139609/b139609.txt">Table of n, a(n) for n = 0..5000</a>
%H A139609 <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%H A139609 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A139609 a(n) = A057145(n+2,9).
%F A139609 G.f.: 9*(1+3*x)/(x-1)^2. - _R. J. Mathar_, Jul 28 2016
%F A139609 From _Elmo R. Oliveira_, Apr 16 2024: (Start)
%F A139609 E.g.f.: 9*exp(x)*(1 + 4*x).
%F A139609 a(n) = 2*a(n-1) - a(n-2) for n >= 2.
%F A139609 a(n) = 9*A016813(n) = A044102(n) + 9 = A152994(n+1) - A152994(n). (End)
%t A139609 Range[9, 7000, 36] (* _Vladimir Joseph Stephan Orlovsky_, Jul 23 2011 *)
%t A139609 36*Range[0,50]+9 (* or *) LinearRecurrence[{2,-1},{9,45},50] (* _Harvey P. Dale_, Jan 04 2018 *)
%o A139609 (Magma) [9*(4*n + 1): n in [0..60]]; // _Vincenzo Librandi_, Jul 23 2011
%o A139609 (PARI) a(n)=36*n+9 \\ _Charles R Greathouse IV_, Oct 05 2011
%Y A139609 Cf. A016813, A044102, A057145, A139600, A152994.
%K A139609 easy,nonn
%O A139609 0,1
%A A139609 _Omar E. Pol_, Apr 27 2008