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 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. 0
 0, 0, 54, 174, 372, 660, 1050, 1554, 2184, 2952, 3870, 4950, 6204, 7644, 9282, 11130, 13200, 15504, 18054, 20862, 23940, 27300, 30954, 34914, 39192, 43800, 48750, 54054, 59724, 65772, 72210, 79050, 86304, 93984, 102102, 110670, 119700 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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. REFERENCES Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.1 Geometric probability constants, p. 482. LINKS Eric Weisstein's MathWorld, Square Division by Lines Eric Weisstein's MathWorld, Cube Division by Planes Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Colin Barker, Oct 09 2014 G.f.: -6*x^2*(7*x-9) / (x-1)^4. - Colin Barker, Oct 09 2014 MATHEMATICA a[n_] := (2*n+23)*n*(n-1); Table[a[n], {n, 0, 40}] PROG (PARI) concat([0, 0], Vec(-6*x^2*(7*x-9)/(x-1)^4 + O(x^100))) \\ Colin Barker, Oct 09 2014 CROSSREFS Sequence in context: A044767 A250792 A044980 * A157428 A068380 A187299 Adjacent sequences:  A248595 A248596 A248597 * A248599 A248600 A248601 KEYWORD nonn,easy AUTHOR Jean-François Alcover, Oct 09 2014 STATUS approved

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Last modified December 16 00:33 EST 2019. Contains 330013 sequences. (Running on oeis4.)