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 A047672 #15 Aug 28 2025 10:31:09
%S A047672 1,10,37,94,193,346,565,862,1249,1738,2341,3070,3937,4954,6133,7486,
%T A047672 9025,10762,12709,14878,17281,19930,22837,26014,29473,33226,37285,
%U A047672 41662,46369,51418,56821,62590,68737,75274,82213,89566,97345,105562,114229,123358,132961
%N A047672 Row 3 of square array defined in A047671.
%H A047672 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A047672 a(n) = 2*n^3 - 3*n^2 + 4*n - 2.
%F A047672 From _Elmo R. Oliveira_, Aug 28 2025: (Start)
%F A047672 G.f.: x*(1 + 6*x + 3*x^2 + 2*x^3)/(1-x)^4.
%F A047672 E.g.f.: 2 + exp(x)*(-2 + 3*x + 3*x^2 + 2*x^3).
%F A047672 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4. (End)
%t A047672 lst={};Do[s0=n^3;s1=(n+1)^3;AppendTo[lst,(s1+s0)+n],{n,0,5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Feb 19 2009 *)
%o A047672 (PARI) vector(50, n, 2*n^3 - 3*n^2 + 4*n - 2) \\ _Michel Marcus_, Jan 07 2015
%o A047672 (PARI) my(x='x+O('x^42)); Vec(x*(1+6*x+3*x^2+2*x^3)/(x-1)^4) \\ _Elmo R. Oliveira_, Aug 28 2025
%K A047672 nonn,easy,changed
%O A047672 1,2
%A A047672 _N. J. A. Sloane_
%E A047672 More terms from _Elmo R. Oliveira_, Aug 28 2025