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%I #4 Oct 30 2015 08:04:15
%S 1,1,2,1,2,3,1,2,3,5,1,2,3,11,8,1,2,3,11,17,13,1,2,3,11,17,49,21,1,2,
%T 3,11,17,70,80,34,1,2,3,11,17,70,108,249,55,1,2,3,11,17,70,108,423,
%U 414,89,1,2,3,11,17,70,108,483,664,1237,144,1,2,3,11,17,70,108,483,739,2667
%N T(n,k)=Number of length n arrays of permutations of 0..n-1 with each element moved by -k to k places and the total absolute value of displacements not greater than n.
%C Table starts
%C ...1.....1......1......1......1......1......1......1......1......1......1
%C ...2.....2......2......2......2......2......2......2......2......2......2
%C ...3.....3......3......3......3......3......3......3......3......3......3
%C ...5....11.....11.....11.....11.....11.....11.....11.....11.....11.....11
%C ...8....17.....17.....17.....17.....17.....17.....17.....17.....17.....17
%C ..13....49.....70.....70.....70.....70.....70.....70.....70.....70.....70
%C ..21....80....108....108....108....108....108....108....108....108....108
%C ..34...249....423....483....483....483....483....483....483....483....483
%C ..55...414....664....739....739....739....739....739....739....739....739
%C ..89..1237...2667...3271...3426...3426...3426...3426...3426...3426...3426
%C .144..2099...4221...5030...5216...5216...5216...5216...5216...5216...5216
%C .233..6314..17124..22666..24476..24854..24854..24854..24854..24854..24854
%C .377.10846..27252..34917..37233..37674..37674..37674..37674..37674..37674
%C .610.32254.110935.158899.176887.181883.182772.182772.182772.182772.182772
%C .987.56036.177405.245151.268945.275132.276148.276148.276148.276148.276148
%H R. H. Hardin, <a href="/A263939/b263939.txt">Table of n, a(n) for n = 1..653</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%e Some solutions for n=7 k=4
%e ..2....0....0....0....1....0....0....0....0....0....0....0....1....1....0....0
%e ..1....2....1....1....2....1....2....1....1....1....2....1....0....3....1....3
%e ..0....3....3....3....0....4....4....3....2....3....1....2....2....2....2....2
%e ..3....1....2....2....4....3....3....2....5....5....5....3....5....0....5....1
%e ..5....4....5....4....3....2....1....5....4....4....4....4....3....4....4....4
%e ..4....6....6....5....5....6....5....4....6....2....3....5....4....5....3....5
%e ..6....5....4....6....6....5....6....6....3....6....6....6....6....6....6....6
%Y Column 1 is A000045(n+1).
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_, Oct 30 2015
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