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A263424 T(n,k)=Number of nXk arrays of permutations of 0..n*k-1 with each element moved a city block distance of 0 or 2.

%I A263424 #4 Oct 17 2015 15:53:48
%S A263424 1,1,1,2,4,2,4,36,36,4,6,196,1272,196,6,9,961,26244,26244,961,9,15,
%T A263424 5329,532620,1993744,532620,5329,15,25,29584,11751184,141086884,
%U A263424 141086884,11751184,29584,25,40,160000,256052940,10808097444,34502512032
%N A263424 T(n,k)=Number of nXk arrays of permutations of 0..n*k-1 with each element moved a city block distance of 0 or 2.
%C A263424 Table starts
%C A263424 ..1......1..........2............4.............6.............9...............15
%C A263424 ..1......4.........36..........196...........961..........5329............29584
%C A263424 ..2.....36.......1272........26244........532620......11751184........256052940
%C A263424 ..4....196......26244......1993744.....141086884...10808097444.....831331827076
%C A263424 ..6....961.....532620....141086884...34502512032.9414955824400.2581177525941432
%C A263424 ..9...5329...11751184..10808097444.9414955824400
%C A263424 .15..29584..256052940.831331827076
%C A263424 .25.160000.5521233025
%C A263424 .40.868624
%C A263424 .64
%H A263424 R. H. Hardin, <a href="/A263424/b263424.txt">Table of n, a(n) for n = 1..60</a>
%F A263424 Empirical for column k:
%F A263424 k=1: a(n) = a(n-1) +a(n-3) +a(n-4)
%F A263424 k=2: [order 15]
%F A263424 k=3: [order 64]
%e A263424 Some solutions for n=3 k=4
%e A263424 ..2..9..0..1....8..9..7..6....0..4..7..6....8..4..0..3....5..6.10.11
%e A263424 ..4..7.11.10....1..5.11..2....9..2..1.10....1..5.11..7....1..0..4..7
%e A263424 ..5..6..8..3....0..4.10..3....5.11..8..3...10..9..2..6....8..9..2..3
%Y A263424 Column 1 is A006498.
%K A263424 nonn,tabl
%O A263424 1,4
%A A263424 _R. H. Hardin_, Oct 17 2015