1,4

Suggested by Question 8 on the Mathpath 2006 Qualifying Quiz, which says:

"You are given 5 dots arranged on a circle and told to draw segments between pairs of the

points to connect all the dots. It is always possible to do this with 4 segments. However,

suppose you are required to use 5 segments, that is, the dots should not all be connected until

you draw your fifth segment. For instance, if the dots are numbered 1,2,3,4,5, one way to do

this is to draw the following sequence of segments: 12, 34, 24, 13, 35. Another sequence

would be 34, 13, 12, 24, 35; it uses the same segments but in a different order. (But careful:

some other orders of these 5 segments do not count; why not?). Another sequence, using

some different edges, is 23, 24, 25, 34, 15. Note that you may not draw the same segment

twice. In other words, 12, 23, 23, 34, 45 uses only 4 segments, not 5.

How many sequences are there which take 5 segments to connect all 5 dots?"

The sequence arises if we replace "5" by "n".

Mathpath 2006, Qualifying Quiz

The answer to Question 8 is (presumably) a(5) = 7200.

f:=proc(n) local t1, t2, t3; t1:=binomial(n-1, 2); t2:=t1!/(t1-n+1)!; t3:=n*(n-1)*t2; end;

Sequence in context: A111782 A054557 A103861 this_sequence A093272 A105347 A093236

Adjacent sequences: A119747 A119748 A119749 this_sequence A119751 A119752 A119753

nonn

njas, Aug 01 2006