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A263905 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 2*(n-1).

%I A263905 #4 Oct 29 2015 07:45:14
%S A263905 1,1,2,1,2,3,1,2,6,5,1,2,6,13,8,1,2,6,20,31,13,1,2,6,20,61,73,21,1,2,
%T A263905 6,20,76,185,172,34,1,2,6,20,76,269,577,399,55,1,2,6,20,76,300,979,
%U A263905 1788,932,89,1,2,6,20,76,300,1189,3552,5540,2177,144,1,2,6,20,76,300,1252
%N A263905 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 2*(n-1).
%C A263905 Table starts
%C A263905 ..1....1.....1.....1.....1.....1.....1......1......1......1......1......1
%C A263905 ..2....2.....2.....2.....2.....2.....2......2......2......2......2......2
%C A263905 ..3....6.....6.....6.....6.....6.....6......6......6......6......6......6
%C A263905 ..5...13....20....20....20....20....20.....20.....20.....20.....20.....20
%C A263905 ..8...31....61....76....76....76....76.....76.....76.....76.....76.....76
%C A263905 .13...73...185...269...300...300...300....300....300....300....300....300
%C A263905 .21..172...577...979..1189..1252..1252...1252...1252...1252...1252...1252
%C A263905 .34..399..1788..3552..4701..5197..5324...5324...5324...5324...5324...5324
%C A263905 .55..932..5540.13068.18754.21735.22869..23124..23124..23124..23124..23124
%C A263905 .89.2177.17165.47999.75243.91151.98497.101037.101548.101548.101548.101548
%H A263905 R. H. Hardin, <a href="/A263905/b263905.txt">Table of n, a(n) for n = 1..617</a>
%F A263905 Empirical for column k:
%F A263905 k=1: a(n) = a(n-1) +a(n-2)
%F A263905 k=2: a(n) = 2*a(n-1) +2*a(n-3) +a(n-4) -3*a(n-5) -2*a(n-7) +a(n-9)
%e A263905 Some solutions for n=7 k=4
%e A263905 ..3....0....3....2....4....0....3....0....0....1....4....0....3....0....2....1
%e A263905 ..0....3....1....1....1....1....1....5....1....3....0....2....0....2....1....3
%e A263905 ..2....1....5....5....0....3....0....3....4....2....2....1....4....4....4....2
%e A263905 ..6....4....2....0....3....2....6....4....5....6....1....5....2....1....0....6
%e A263905 ..1....5....0....3....6....4....4....1....6....0....5....6....5....3....6....0
%e A263905 ..4....6....4....4....2....5....2....2....2....4....6....4....1....6....5....5
%e A263905 ..5....2....6....6....5....6....5....6....3....5....3....3....6....5....3....4
%Y A263905 Column 1 is A000045(n+1).
%K A263905 nonn,tabl
%O A263905 1,3
%A A263905 _R. H. Hardin_, Oct 29 2015