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 A189890 #38 Sep 08 2022 08:45:56
%S A189890 2,4,10,23,46,82,134,205,298,416,562,739,950,1198,1486,1817,2194,2620,
%T A189890 3098,3631,4222,4874,5590,6373,7226,8152,9154,10235,11398,12646,13982,
%U A189890 15409,16930,18548,20266,22087,24014,26050,28198,30461,32842,35344,37970,40723,43606,46622
%N A189890 a(n) = (n^3 - 2*n^2 + 3*n + 2)/2.
%C A189890 Order preserving identity difference partial one - one transformation semigroup, OIDI_n is defined if for each transformation, alpha, x<= y implies xalpha <= yalpha, for all x,y in X_n (set of natural numbers) and also the absolute value of the difference between max(Im(alpha)) and min(Im(alpha)) is less than or equal to one with non-isolation property.
%H A189890 Vincenzo Librandi, <a href="/A189890/b189890.txt">Table of n, a(n) for n = 1..1000</a>
%H A189890 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A189890 G.f.: -x*(-2+4*x-6*x^2+x^3) / (x-1)^4. - _R. J. Mathar_, Jun 20 2011
%F A189890 E.g.f.: 4*(-2 + (2 + 2*x + x^2 + x^3)*exp(x)). - _G. C. Greubel_, Jan 13 2018
%F A189890 a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - _Wesley Ivan Hurt_, Apr 23 2021
%e A189890 For n = 4, a(4) = (4^3-2*4^2+3*4+2)/2 = 46/2 = 23.
%t A189890 Table[(n^3-2*n^2+3*n+2)/2, {n,1,50}] (* or *) LinearRecurrence[{4,-6,4, -1}, {2,4,10,23}, 50] (* _G. C. Greubel_, Jan 13 2018 *)
%o A189890 (Magma) [(n^3-2*n^2+3*n+2)/2: n in [1..50]]; // _Vincenzo Librandi_, May 07 2011
%o A189890 (PARI) a(n)=(n^3-2*n^2+3*n+2)/2 \\ _Charles R Greathouse IV_, Oct 16 2015
%Y A189890 Cf. A188947, A188377.
%K A189890 nonn,easy
%O A189890 1,1
%A A189890 _Adeniji, Adenike_ and Samuel Makanjuola(somakanjuola(AT)unilorin.edu.ng), Apr 30 2011