[seqfan] Re: Permutations along all diagonals and subdiagonals

[Alois Heinz]

Ron Hardin schrieb:
> Here's three series out of it, I guess
>
> %S XXX 0,1,4,9,12,25,60,121,220,441,924,1849,3612,7225,14620,29241,58140,
> %T XXX 116281,233244,466489,931612,1863225,3729180,7458361,14911260,29822521,
> %U XXX 59655964,119311929,238602012,477204025,954451740,1908903481,3817719580
> %N XXX Number of nX3 arrays with every diagonal and anti-diagonal of length L 
> containing a permutation of 1..L
>   
This sequence seems to have a simple gf:
   -(-x-2*x^2-2*x^3+4*x^4)*x^3 / (1-2*x+x^2-2*x^3-2*x^4+4*x^5)

Alois