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ID Number: A014206
Sequence: 2,4,8,14,22,32,44,58,74,92,112,134,158,184,212,242,274,308,
344,382,422,464,508,554,602,652,704,758,814,872,932,994,
1058,1124,1192,1262,1334,1408,1484,1562,1642,1724
Name: n^2+n+2.
Comments: Draw n+1 circles in the plane; sequence gives maximal number of regions
into which the plane is divided.
References L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 73, Problem 3.
Indiana School Mathematics Journal, vol. 14, no. 4, 1979, p. 4.
J. D. E. Konhauser et al., Which Way Did the Bicycle Go?, MAA 1996, p. 177.
A. M. Yaglom and I. M. Yaglom: Challenging Mathematical Problems with
Elementary Solutions. Vol. I. Combinatorial Analysis and
Probability Theory. New York: Dover Publications, Inc., 1987, p. 13,
#44 (1st. publ.: San Francisco: Holden-Day, Inc., 1964)
Links: Parabola, vol. 24, no. 1, 1988, p. 22, Problem #Q736.
E. W. Weisstein, Link to a section of The World of Mathematics.
Formula: G.f.: 2*x*(x^2-x+1)/(1-x)^3.
n hyperspheres divide R^k into at most C(n-1,k) + Sum_{i=0..k} C(n,i)
regions.
Maple: A014206:=n->n^2+n+2;
See also: Cf. A014206 (dim 2), A046127 (dim 3), A059173 (dim 4), A059174 (dim 5). A
row of A059250.
Cf. A000124, A051890. Also A033547=partial sums of A014206.
Keywords: nonn,easy,nice
Offset: 0
Author(s): njas
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