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%I #7 May 19 2024 20:40:43
%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,2,1,0,0,0,0,1,5,10,
%T 3,0,0,0,0,1,5,37,31,11,0,0,0,0,1,5,66,116,134,31,0,0,0,0,1,5,66,267,
%U 572,439,93,0,0,0,0,1,5,66,392,1721,2042,1604,248,0,0,0,0,1,5,66,392,3522
%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 exactly two more elements moved upwards than downwards.
%C Table starts
%C .0...0.....0......0......0.......0.......0........0........0........0........0
%C .0...0.....0......0......0.......0.......0........0........0........0........0
%C .0...0.....0......0......0.......0.......0........0........0........0........0
%C .0...0.....1......1......1.......1.......1........1........1........1........1
%C .0...0.....2......5......5.......5.......5........5........5........5........5
%C .0...1....10.....37.....66......66......66.......66.......66.......66.......66
%C .0...3....31....116....267.....392.....392......392......392......392......392
%C .0..11...134....572...1721....3522....4859.....4859.....4859.....4859.....4859
%C .0..31...439...2042...6618...15699...26994....34659....34659....34659....34659
%C .0..93..1604...9298..35203..104014..232208...383663...482272...482272...482272
%C .0.248..5088..35064.144762..463811.1161998..2245936..3388097..4099634..4099634
%C .0.670.17115.149613.741173.2735525.8246455.19777342.37109391.54900952.65762489
%H R. H. Hardin, <a href="/A263787/b263787.txt">Table of n, a(n) for n = 1..424</a>
%e Some solutions for n=7, k=4
%e ..3....3....4....3....1....3....4....3....0....4....0....4....1....0....3....4
%e ..5....1....0....1....0....0....0....0....4....1....5....0....5....5....0....1
%e ..0....6....1....6....6....6....6....1....1....6....6....6....0....1....1....0
%e ..1....0....2....2....2....1....1....5....6....2....2....1....2....2....2....2
%e ..2....2....5....0....3....4....2....2....2....0....1....3....3....6....6....3
%e ..4....4....3....4....5....2....5....4....3....3....4....5....4....3....5....5
%e ..6....5....6....5....4....5....3....6....5....5....3....2....6....4....4....6
%Y Diagonal is A169934.
%K nonn,tabl
%O 1,26
%A _R. H. Hardin_, Oct 26 2015
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