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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. 1
 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 Harvey P. Dale, Table of n, a(n) for n = 0..1000 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}] LinearRecurrence[{4, -6, 4, -1}, {0, 0, 54, 174}, 50] (* Harvey P. Dale, Mar 17 2022 *) 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 A187299 A288626 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 October 4 04:26 EDT 2022. Contains 357237 sequences. (Running on oeis4.)