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 A166151 #31 Feb 20 2023 03:09:55 %S A166151 2,12,27,47,72,102,137,177,222,272,327,387,452,522,597,677,762,852, %T A166151 947,1047,1152,1262,1377,1497,1622,1752,1887,2027,2172,2322,2477,2637, %U A166151 2802,2972,3147,3327,3512,3702,3897,4097,4302,4512,4727,4947,5172,5402,5637 %N A166151 a(n) = (5*n^2 + 5*n - 6)/2. %H A166151 Vincenzo Librandi, <a href="/A166151/b166151.txt">Table of n, a(n) for n = 1..1000</a> %H A166151 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1). %F A166151 From _R. J. Mathar_, Oct 14 2009: (Start) %F A166151 a(n) = 5*n*(n+1)/2 - 3. %F A166151 a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). %F A166151 G.f.: x*(-2-6*x+3*x^2)/(x-1)^3. (End) %F A166151 E.g.f.: (1/2)*(5*x^2 + 10*x - 6)*exp(x) + 6. - _G. C. Greubel_, May 01 2016 %F A166151 Sum_{n>=1} 1/a(n) = 1/3 + (2*Pi/sqrt(145))*tan(sqrt(29/5)*Pi/2). - _Amiram Eldar_, Feb 20 2023 %t A166151 Table[(5 n^2 + 5 n - 6)/2, {n, 50}] (* or *) CoefficientList[Series[(- 2 - 6 x + 3 x^2)/(x - 1)^3, {x, 0, 50}], x] (* _Vincenzo Librandi_, Sep 13 2013 *) %t A166151 LinearRecurrence[{3,-3,1},{2,12,27}, 50] (* _G. C. Greubel_, May 01 2016 *) %o A166151 (Magma) [(5*n^2 + 5*n - 6)/2: n in [1..50]]; // _Vincenzo Librandi_, Sep 13 2013 %o A166151 (PARI) a(n)=(5*n^2+5*n-6)/2 \\ _Charles R Greathouse IV_, May 02 2016 %K A166151 nonn,easy %O A166151 1,1 %A A166151 _Vincenzo Librandi_, Oct 08 2009