[seqfan] Re: Excess permutation left moves over right moves

William Keith wjk26 at drexel.edu
Sun Jul 18 01:30:37 CEST 2010


Suppose you take A000006 through A000010 and produce the linear recursions associated to those, then form the jagged table of the signed coefficients that appear in the recursions with them and the recursion in A000011 through  A000013, i.e. these:

> a(n)=5*a(n-1)-9*a(n-2)+7*a(n-3)-2*a(n-4)

(giving 5, -9, 7, -2)

Perhaps there might be an interesting Pascaline rule on the coefficients thus arranged?  It would be especially interesting if it could be proved that the recurrences hold indefinitely, which it seems plausible to me that they would.

William Keith


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