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 A248598 #16 Feb 16 2025 08:33:23
%S A248598 0,0,54,174,372,660,1050,1554,2184,2952,3870,4950,6204,7644,9282,
%T A248598 11130,13200,15504,18054,20862,23940,27300,30954,34914,39192,43800,
%U A248598 48750,54054,59724,65772,72210,79050,86304,93984,102102,110670,119700
%N A248598 a(n) = (2*n+23)*n*(n-1), a coefficient appearing in the formula a(n)*Pi/324+n+1 giving the average number of regions into which n random planes divide the cube.
%C A248598 The analog formula giving the average number of regions into which n random lines divide the square is n*(n-1)*Pi/16+n+1.
%D A248598 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.1 Geometric probability constants, p. 482.
%H A248598 Harvey P. Dale, <a href="/A248598/b248598.txt">Table of n, a(n) for n = 0..1000</a>
%H A248598 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/SquareDivisionbyLines.html">Square Division by Lines</a>
%H A248598 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/CubeDivisionbyPlanes.html">Cube Division by Planes</a>
%H A248598 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A248598 a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - _Colin Barker_, Oct 09 2014
%F A248598 G.f.: -6*x^2*(7*x-9) / (x-1)^4. - _Colin Barker_, Oct 09 2014
%t A248598 a[n_] := (2*n+23)*n*(n-1); Table[a[n], {n, 0, 40}]
%t A248598 LinearRecurrence[{4,-6,4,-1},{0,0,54,174},50] (* _Harvey P. Dale_, Mar 17 2022 *)
%o A248598 (PARI) concat([0,0], Vec(-6*x^2*(7*x-9)/(x-1)^4 + O(x^100))) \\ _Colin Barker_, Oct 09 2014
%K A248598 nonn,easy
%O A248598 0,3
%A A248598 _Jean-François Alcover_, Oct 09 2014