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A263764 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 one more element moved upwards than downwards.

%I A263764 #6 Jul 23 2025 15:38:07
%S A263764 0,0,0,0,0,0,0,0,1,0,0,0,1,2,0,0,0,1,4,6,0,0,0,1,4,19,14,0,0,0,1,4,31,
%T A263764 50,38,0,0,0,1,4,31,106,165,88,0,0,0,1,4,31,146,485,476,217,0,0,0,1,4,
%U A263764 31,146,961,1546,1543,506,0,0,0,1,4,31,146,1289,3662,6083,4544,1209,0,0,0,1
%N A263764 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 one more element moved upwards than downwards.
%C A263764 Table starts
%C A263764 .0...0....0.....0.....0......0......0......0......0......0......0......0......0
%C A263764 .0...0....0.....0.....0......0......0......0......0......0......0......0......0
%C A263764 .0...1....1.....1.....1......1......1......1......1......1......1......1......1
%C A263764 .0...2....4.....4.....4......4......4......4......4......4......4......4......4
%C A263764 .0...6...19....31....31.....31.....31.....31.....31.....31.....31.....31.....31
%C A263764 .0..14...50...106...146....146....146....146....146....146....146....146....146
%C A263764 .0..38..165...485...961...1289...1289...1289...1289...1289...1289...1289...1289
%C A263764 .0..88..476..1546..3662...6152...7736...7736...7736...7736...7736...7736...7736
%C A263764 .0.217.1543..6083.18444..41747..68811..85831..85831..85831..85831..85831..85831
%C A263764 .0.506.4544.21020.69848.181272.354568.533302.641302.641302.641302.641302.641302
%H A263764 R. H. Hardin, <a href="/A263764/b263764.txt">Table of n, a(n) for n = 1..424</a>
%e A263764 Some solutions for n=7 k=4
%e A263764 ..1....4....0....1....0....0....3....3....4....0....4....3....2....0....3....0
%e A263764 ..2....0....1....5....4....5....4....0....2....4....5....0....0....1....5....4
%e A263764 ..0....1....6....0....1....1....1....6....1....2....0....6....4....2....0....6
%e A263764 ..6....6....4....6....3....3....2....2....0....1....6....1....6....6....1....3
%e A263764 ..3....5....3....2....2....2....0....5....3....3....1....5....3....4....2....1
%e A263764 ..4....3....2....4....5....6....5....1....5....5....2....4....1....3....6....2
%e A263764 ..5....2....5....3....6....4....6....4....6....6....3....2....5....5....4....5
%Y A263764 Diagonal is A179562.
%K A263764 nonn,tabl
%O A263764 1,14
%A A263764 _R. H. Hardin_, Oct 25 2015