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%I #6 Nov 10 2015 11:41:35
%S 4,17,9,56,96,25,172,623,596,64,561,3736,7949,3610,169,1826,24908,
%T 97332,97520,21997,441,5880,163505,1333336,2407816,1210573,133836,
%U 1156,18993,1056337,17998869,68008846,60472721,14973263,814609,3025,61424,6877345
%N T(n,k)=Number of (n+1)X(k+1) arrays of permutations of 0..(n+1)*(k+1)-1 with each element having directed index change 0,0 0,1 1,0 -1,0 or 0,-2.
%C Table starts
%C ....4.......17..........56............172...............561...............1826
%C ....9.......96.........623...........3736.............24908.............163505
%C ...25......596........7949..........97332...........1333336...........17998869
%C ...64.....3610.......97520........2407816..........68008846.........1883268032
%C ..169....21997.....1210573.......60472721........3516298221.......200034582505
%C ..441...133836....14973263.....1511983080......181148689096.....21168809029549
%C .1156...814609...185410184....37854981564.....9342273315041...2243001383143442
%C .3025..4957760..2295059475...947369885896...481661295203904.237592988053853489
%C .7921.30173957.28412159649.23712132417625.24835326206594357
%H R. H. Hardin, <a href="/A264217/b264217.txt">Table of n, a(n) for n = 1..97</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) +2*a(n-2) -a(n-3)
%F k=2: [order 8]
%F k=3: [order 23]
%F Empirical for row n:
%F n=1: a(n) = 2*a(n-1) +2*a(n-2) +6*a(n-3) +2*a(n-4) -2*a(n-5) -a(n-6)
%F n=2: [order 46]
%e Some solutions for n=3 k=4
%e ..0..3..2..8..4....2..0..1..8..3....0..3..4..2..9....0..3..1..2..4
%e ..5..1..6..7..9....5..6..9..7..4...10..1..6..7.14...10..5..7..8..9
%e .10.11.12.18.14...15.11.12.18.14....5.16.17..8.19...12..6.11.13.19
%e .17.15.16.13.19...10.16.17.13.19...15.11.12.13.18...15.16.17.18.14
%Y Column 1 is A007598(n+2).
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 08 2015
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