

A248598


a(n) = (2*n+23)*n*(n1), 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
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OFFSET

0,3


COMMENTS

The analog formula giving the average number of regions into which n random lines divide the square is n*(n1)*Pi/16+n+1.


REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.1 Geometric probability constants, p. 482.


LINKS

Table of n, a(n) for n=0..36.
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(n1)6*a(n2)+4*a(n3)a(n4).  Colin Barker, Oct 09 2014
G.f.: 6*x^2*(7*x9) / (x1)^4.  Colin Barker, Oct 09 2014


MATHEMATICA

a[n_] := (2*n+23)*n*(n1); Table[a[n], {n, 0, 40}]


PROG

(PARI) concat([0, 0], Vec(6*x^2*(7*x9)/(x1)^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

JeanFrançois Alcover, Oct 09 2014


STATUS

approved



