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 A166154 #31 Feb 20 2023 03:09:35 %S A166154 2,16,37,65,100,142,191,247,310,380,457,541,632,730,835,947,1066,1192, %T A166154 1325,1465,1612,1766,1927,2095,2270,2452,2641,2837,3040,3250,3467, %U A166154 3691,3922,4160,4405,4657,4916,5182,5455,5735,6022,6316,6617,6925,7240,7562 %N A166154 a(n) = 7*n*(n+1)/2 - 5. %H A166154 Vincenzo Librandi, <a href="/A166154/b166154.txt">Table of n, a(n) for n = 1..1000</a> %H A166154 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1). %F A166154 a(n) = A166146(n)+1. %F A166154 a(n) = a(n-1)+7*n = 3*a(n-1) -3*a(n-2) +a(n-3). %F A166154 G.f.: x*(-2-10*x+5*x^2)/(x-1)^3. %F A166154 E.g.f.: (7/2)*((x^2 + 2*x - 5)*exp(x) + 5). - _G. C. Greubel_, May 01 2016 %F A166154 Sum_{n>=1} 1/a(n) = 1/5 + (2*Pi/sqrt(329))*tan(sqrt(47/7)*Pi/2). - _Amiram Eldar_, Feb 20 2023 %t A166154 Table[7 n (n + 1)/2 - 5, {n, 100}] (* or *) CoefficientList[Series[(- 2 - 10 x + 5 x^2) / (x - 1)^3, {x, 0, 50}], x] (* _Vincenzo Librandi_, Sep 13 2013 *) %t A166154 LinearRecurrence[{3,-3,1}, {2,16,37}, 50] (* _G. C. Greubel_, May 01 2016 *) %o A166154 (Magma) [7*n*(n+1)/2-5: n in [1..50]]; // _Vincenzo Librandi_, Sep 13 2013 %o A166154 (PARI) a(n)=7*n*(n+1)/2-5 \\ _Charles R Greathouse IV_, May 02 2016 %Y A166154 Cf. A166146. %K A166154 nonn,easy %O A166154 1,1 %A A166154 _Vincenzo Librandi_, Oct 08 2009 %E A166154 Definition replaced by polynomial, A-number corrected, formulas added by _R. J. Mathar_, Oct 12 2009