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 A179986 #69 Sep 08 2022 08:45:54
%S A179986 0,6,19,39,66,100,141,189,244,306,375,451,534,624,721,825,936,1054,
%T A179986 1179,1311,1450,1596,1749,1909,2076,2250,2431,2619,2814,3016,3225,
%U A179986 3441,3664,3894,4131,4375,4626,4884,5149,5421,5700,5986,6279,6579,6886
%N A179986 Second 9-gonal (or nonagonal) numbers: a(n) = n*(7*n+5)/2.
%C A179986 This sequence is a bisection of A118277 (even part).
%C A179986 Sequence found by reading the line from 0, in the direction 0, 19... and the line from 6, in the direction 6, 39,..., in the square spiral whose vertices are the generalized 9-gonal numbers A118277. - _Omar E. Pol_, Jul 24 2012
%C A179986 The early part of this sequence is a strikingly close approximation to the early part of A100752. - _Peter Munn_, Nov 14 2019
%H A179986 Vincenzo Librandi, <a href="/A179986/b179986.txt">Table of n, a(n) for n = 0..1000</a>
%H A179986 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A179986 G.f.: x*(6 + x)/(1 - x)^3.
%F A179986 a(n) = Sum_{i=0..(n-1)} A017053(i) for n>0.
%F A179986 a(-n) = A001106(n).
%F A179986 Sum_{i=0..n} (a(n)+i)^2 = ( Sum_{i=(n+1)..2*n} (a(n)+i)^2 ) + 21*A000217(n)^2 for n>0.
%F A179986 a(n) = a(n-1)+7*n-1 for n>0, with a(0)=0. - _Vincenzo Librandi_, Feb 05 2011
%F A179986 a(0)=0, a(1)=6, a(2)=19; for n>2, a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). - _Harvey P. Dale_, Aug 19 2011
%F A179986 a(n) = A174738(7n+5). - _Philippe Deléham_, Mar 26 2013
%F A179986 a(n) = A001477(n) + 2*A000290(n) + 3*A000217(n). - _J. M. Bergot_, Apr 25 2014
%F A179986 a(n) = A055998(4*n) - A055998(3*n). - _Bruno Berselli_, Sep 23 2016
%F A179986 E.g.f.: (x/2)*(12 + 7*x)*exp(x). - _G. C. Greubel_, Aug 19 2017
%t A179986 f[n_] := n (7 n + 5)/2; f[Range[0, 60]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 05 2011*)
%t A179986 LinearRecurrence[{3, -3, 1}, {0, 6, 19}, 60] (* or *) Array[(#(7# + 5))/2&, 60, 0] (* _Harvey P. Dale_, Aug 19 2011 *)
%t A179986 CoefficientList[Series[x (6 + x)/(1 - x)^3, {x, 0, 60}], x] (* _Vincenzo Librandi_, Oct 15 2012 *)
%o A179986 (Magma) [n*(7*n+5)/2: n in [0..50]]; // _Bruno Berselli_, Sep 23 2016
%o A179986 (Magma) I:=[0, 6, 19]; [n le 3 select I[n] else 3*Self(n-1) -3*Self(n-2) +Self(n-3): n in [1..60]]; // _Vincenzo Librandi_, Oct 15 2012
%o A179986 (PARI) a(n)=n*(7*n+5)/2 \\ _Charles R Greathouse IV_, Sep 24 2015
%Y A179986 Cf. second k-gonal numbers: A005449 (k=5), A014105 (k=6), A147875 (k=7), A045944 (k=8), this sequence (k=9), A033954 (k=10), A062728 (k=11), A135705 (k=12).
%Y A179986 Cf. A001106, A022264, A022265, A024966, A055998, A100752, A174738, A186029, A218471.
%K A179986 nonn,easy
%O A179986 0,2
%A A179986 _Bruno Berselli_, Jan 13 2011