Jason (jcreed) wrote,

More actual getting work done today.

In my spare hours I sometimes enjoy playing a game called "WTF, The On-Line Encyclopedia of Integer Sequences?". It goes like this.

Step one: think of a combinatorial problem. Such as, count the graph-like structures like
   / \ 
  /   \
 |     |
/ \    |
\ /    |
 |     |
 |    / \
 |    \ /
 |     |
  \   /
   \ /

where, viewing this as a Feynman-diagram-like history of a little particle, the particle splits up and joins back up a few times.

Step two: figure out a recurrence well enough to crank out a few terms manually. Such as, the number of tree structures above that begin and end with one particle, and which have 0, 2, 4, 6, 8 interactions are 1,1,5,61,1385. (This is ignoring "concurrency" because I don't know how to efficiently count them otherwise --- that is, the diagram above and its mirror image are considered different, and indeed there are a couple other interleavings of the duplication and joining of the two "inner" particles)

Step three: Look that shit up on TOLEoIS.

Step four: WTF, The On-Line Encyclopedia of Integer Sequences? It's the coefficients of the power series for the secant function? Why the heck is that true?
Tags: math, sequences, work
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