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 A118060 #28 Sep 08 2022 08:45:24
%S A118060 1,4060,11481,22264,36409,53916,74785,99016,126609,157564,191881,
%T A118060 229560,270601,315004,362769,413896,468385,526236,587449,652024,
%U A118060 719961,791260,865921,943944,1025329,1110076,1198185,1289656,1384489,1482684,1584241
%N A118060 a(n) = 1681*n^2 - 984*n - 696.
%C A118060 In general, all sequences of equations which contain every positive integer in order exactly once (a pairwise equal summed, ordered partition of the positive integers) may be defined as follows: For all k, let x(k)=A001652(k) and z(k)=A001653(k). Then if we define a(n) to be (x(k)+z(k))n^2-(z(k)-1)n-x(k), the following equation is true: a(n)+(a(n)+1)+...+(a(n)+(x(k)+z(k))n+(2x(k)+z(k)-1)/2)=(a(n)+ (x(k)+z(k))n+(2x(k)+z(k)+1)/2)+...+(a(n)+2(x(k)+z(k))n+x(k)); a(n)+2(x(k)+z(k))n+x(k))=a(n+1)-1; e.g., in this sequence, x(4)=A001652(4)=696 and z(4)=A001653(4)=985; cf. A000290, A118057-A118059, A118061.
%H A118060 Vincenzo Librandi, <a href="/A118060/b118060.txt">Table of n, a(n) for n = 1..1000</a>
%H A118060 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A118060 a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). G.f.: x*(1+4057*x-696*x^2)/(1-x)^3. - _Colin Barker_, Jul 01 2012
%F A118060 a(n)+(a(n)+1)+...+(a(n)+1681n+1188) = (a(n)+1681n+1189)+ ... +a(n+1)-1; a(n+1)-1 = a(n)+3362n+696.
%F A118060 a(n)+(a(n)+1)+...+(a(n)+1681n+1188)=41(41n-12)(41n+29)(82n+17)/2; e.g., 11481+11482+...+17712=90965388=41*111*152*263/2.
%e A118060 a(3)=1681*3^2-984*3-696=11481, a(4)=1681*4^2-984*4-696=22264 and 11481+11482+...+17712=17713+...+22263
%t A118060 CoefficientList[Series[(1+4057*x-696*x^2)/(1-x)^3,{x,0,40}],x] (* _Vincenzo Librandi_, Jul 09 2012 *)
%t A118060 LinearRecurrence[{3,-3,1},{1,4060,11481},40] (* _Harvey P. Dale_, Oct 28 2016 *)
%o A118060 (Magma) [1681*n^2 - 984*n - 696: n in [1..40]]; // _Vincenzo Librandi_, Jul 09 2012
%o A118060 (PARI) a(n)=1681*n^2-984*n-696 \\ _Charles R Greathouse IV_, Jun 17 2017
%K A118060 nonn,easy,less
%O A118060 1,2
%A A118060 _Charlie Marion_, Apr 26 2006
%E A118060 Corrected by _T. D. Noe_, Nov 13 2006