Match Problem

Given $n$ matches, find the number of topologically distinct planar arrangements $T(n)$ which can be made. The first few values are 1, 1, 3, 5, 10, 19, 39, ... (Sloane's A003055).

See also Cigarettes, Matchstick Graph

References

Gardner, M. ``The Problem of the Six Matches.'' In The Unexpected Hanging and Other Mathematical Diversions. Chicago, IL: Chicago University Press, pp. 79-81, 1991.

Sloane, N. J. A. Sequence A003055/M2464 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.