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 A081435 #19 Dec 28 2024 17:52:02
%S A081435 1,5,18,46,95,171,280,428,621,865,1166,1530,1963,2471,3060,3736,4505,
%T A081435 5373,6346,7430,8631,9955,11408,12996,14725,16601,18630,20818,23171,
%U A081435 25695,28396,31280,34353,37621,41090,44766,48655,52763,57096,61660
%N A081435 Diagonal in array of n-gonal numbers A081422.
%C A081435 One of a family of sequences with palindromic generators.
%H A081435 Vincenzo Librandi, <a href="/A081435/b081435.txt">Table of n, a(n) for n = 0..1000</a>
%H A081435 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A081435 a(n) = (2*n^3 +3*n^2 +3*n +2)/2.
%F A081435 G.f.: (1 +3*x^2 -4*x^3)/(1-x)^5.
%F A081435 E.g.f.: (2 +8*x +9*x^2 +2*x^3)*exp(x)/2. - _G. C. Greubel_, Aug 14 2019
%p A081435 a := n-> (n+1)*(2*(n+1)^2-3*n)/2; seq(a(n), n = 0..40); # _G. C. Greubel_, Aug 14 2019
%t A081435 Table[(n^3 +(n+1)^3 -1)/2 +1, {n,0,40}] (* _Vladimir Joseph Stephan Orlovsky_, May 04 2011 *)
%t A081435 CoefficientList[Series[(1 +3x^2 -4x^3)/(1-x)^5, {x,0,40}], x] (* _Vincenzo Librandi_, Aug 08 2013 *)
%t A081435 LinearRecurrence[{4,-6,4,-1},{1,5,18,46},40] (* _Harvey P. Dale_, Dec 28 2024 *)
%o A081435 (Magma) [(2*n^3+3*n^2+3*n+2)/2: n in [0..40]]; // _Vincenzo Librandi_, Aug 08 2013
%o A081435 (PARI) vector(40, n, n--; (n+1)*(2*(n+1)^2-3*n)/2) \\ _G. C. Greubel_, Aug 14 2019
%o A081435 (Sage) [(n+1)*(2*(n+1)^2-3*n)/2 for n in (0..40)] # _G. C. Greubel_, Aug 14 2019
%o A081435 (GAP) List([0..40], n-> (n+1)*(2*(n+1)^2-3*n)/2); # _G. C. Greubel_, Aug 14 2019
%Y A081435 Cf. A081434, A081436, A081437.
%K A081435 nonn,easy
%O A081435 0,2
%A A081435 _Paul Barry_, Mar 21 2003