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A263744 T(n,k)=Number of length n arrays of permutations of 0..n-1 with each element moved by -k to k places and equal numbers of elements moved upwards and downwards.

%I A263744 #6 Jul 23 2025 15:36:50
%S A263744 1,1,2,1,2,3,1,2,4,5,1,2,4,10,8,1,2,4,14,19,13,1,2,4,14,36,43,21,1,2,
%T A263744 4,14,46,110,90,34,1,2,4,14,46,214,277,202,55,1,2,4,14,46,282,664,823,
%U A263744 434,89,1,2,4,14,46,282,1118,2516,2292,971,144,1,2,4,14,46,282,1394,5962
%N A263744 T(n,k)=Number of length n arrays of permutations of 0..n-1 with each element moved by -k to k places and equal numbers of elements moved upwards and downwards.
%C A263744 Table starts
%C A263744 ..1...1....1.....1......1......1......1......1......1......1......1......1
%C A263744 ..2...2....2.....2......2......2......2......2......2......2......2......2
%C A263744 ..3...4....4.....4......4......4......4......4......4......4......4......4
%C A263744 ..5..10...14....14.....14.....14.....14.....14.....14.....14.....14.....14
%C A263744 ..8..19...36....46.....46.....46.....46.....46.....46.....46.....46.....46
%C A263744 .13..43..110...214....282....282....282....282....282....282....282....282
%C A263744 .21..90..277...664...1118...1394...1394...1394...1394...1394...1394...1394
%C A263744 .34.202..823..2516...5962..10090..12658..12658..12658..12658..12658..12658
%C A263744 .55.434.2292..7989..21974..44914..68834..83122..83122..83122..83122..83122
%C A263744 .89.971.6862.30299.100324.266476.535262.816882.985730.985730.985730.985730
%H A263744 R. H. Hardin, <a href="/A263744/b263744.txt">Table of n, a(n) for n = 1..424</a>
%e A263744 Some solutions for n=7 k=4
%e A263744 ..3....3....0....2....3....4....2....0....3....4....2....3....3....3....1....1
%e A263744 ..1....0....4....1....1....5....1....2....0....0....3....2....4....2....2....5
%e A263744 ..0....4....5....0....2....3....6....4....2....3....6....0....6....1....0....2
%e A263744 ..4....1....1....3....0....0....5....1....4....1....1....1....1....0....5....0
%e A263744 ..2....5....3....5....4....2....0....3....6....5....0....4....0....4....3....6
%e A263744 ..5....2....6....4....6....1....4....5....1....2....5....5....5....5....4....3
%e A263744 ..6....6....2....6....5....6....3....6....5....6....4....6....2....6....6....4
%Y A263744 Column 1 is A000045(n+1)
%Y A263744 Diagonal is A062868
%K A263744 nonn,tabl
%O A263744 1,3
%A A263744 _R. H. Hardin_, Oct 25 2015