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 A167499 #52 Oct 31 2024 19:56:13
%S A167499 6,8,11,15,20,26,33,41,50,60,71,83,96,110,125,141,158,176,195,215,236,
%T A167499 258,281,305,330,356,383,411,440,470,501,533,566,600,635,671,708,746,
%U A167499 785,825,866,908,951,995,1040,1086,1133,1181,1230,1280,1331,1383,1436,1490
%N A167499 a(n) = n*(n+3)/2 + 6.
%C A167499 Numbers m > 5 such that 8*m - 39 is a square. - _Bruce J. Nicholson_, Jul 25 2017
%H A167499 Vincenzo Librandi, <a href="/A167499/b167499.txt">Table of n, a(n) for n = 0..1000</a>
%H A167499 Ângela Mestre and José Agapito, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL22/Mestre/mestre2.html">Square Matrices Generated by Sequences of Riordan Arrays</a>, Journal of Integer Sequences, Vol. 22 (2019), Article 19.8.4.
%H A167499 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A167499 a(n) = n + a(n-1) + 1, with n > 1, a(1) = 8.
%F A167499 From _Vincenzo Librandi_, Sep 16 2013: (Start)
%F A167499 G.f.: (6 - 10*x + 5*x^2)/(1-x)^3.
%F A167499 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
%F A167499 Sum_{n>=0} 1/a(n) = 2*Pi*tanh(Pi*sqrt(39)/2)/sqrt(39) - 1/5. - _Amiram Eldar_, Jan 17 2021
%F A167499 From _Elmo R. Oliveira_, Oct 31 2024: (Start)
%F A167499 E.g.f.: exp(x)*(6 + 2*x + x^2/2).
%F A167499 a(n) = A187710(n+1)/2. (End)
%p A167499 A167499:=n->n*(n+3)/2+6: seq(A167499(n), n=0..100); # _Wesley Ivan Hurt_, Jul 25 2017
%t A167499 Table[n*(n + 3)/2 + 6, {n, 0, 100}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 03 2011 *)
%t A167499 CoefficientList[Series[(6 - 10 x + 5 x^2) / (1 - x)^3, {x, 0, 60}], x] (* _Vincenzo Librandi_, Sep 16 2013 *)
%t A167499 LinearRecurrence[{3,-3,1},{6,8,11},60] (* _Harvey P. Dale_, Jun 21 2022 *)
%o A167499 (Magma) [n*(n+3)/2+6: n in [0..60]]; // _Vincenzo Librandi_, Sep 16 2013
%o A167499 (PARI) a(n)=n*(n+3)/2+6 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A167499 Cf. A187710.
%K A167499 nonn,easy
%O A167499 0,1
%A A167499 _Vincenzo Librandi_, Nov 07 2009