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A264379 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 2,-2 -1,0 -1,2 1,0 or 0,-1.

%I A264379 #4 Nov 12 2015 08:00:45
%S A264379 1,2,0,4,1,1,6,6,13,0,9,9,80,25,1,15,61,385,441,128,0,25,121,2345,
%T A264379 3778,3249,347,1,40,544,14329,60858,63575,22484,1343,0,64,1357,88264,
%U A264379 711068,1742881,828400,156293,4172,1,104,5100,538417,9407584,45132986,48714516
%N A264379 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 2,-2 -1,0 -1,2 1,0 or 0,-1.
%C A264379 Table starts
%C A264379 .1.....2.......4..........6.............9..............15.................25
%C A264379 .0.....1.......6..........9............61.............121................544
%C A264379 .1....13......80........385..........2345...........14329..............88264
%C A264379 .0....25.....441.......3778.........60858..........711068............9407584
%C A264379 .1...128....3249......63575.......1742881........45132986.........1187897216
%C A264379 .0...347...22484.....828400......48714516......2546661201.......135926940964
%C A264379 .1..1343..156293...11888603....1363452981....149731056598.....16353452350876
%C A264379 .0..4172.1097881..163298870...38221084820...8620411258657...1906883090233889
%C A264379 .1.14711.7657324.2275569624.1068788896516.499872831041401.225710195773223581
%H A264379 R. H. Hardin, <a href="/A264379/b264379.txt">Table of n, a(n) for n = 1..144</a>
%F A264379 Empirical for column k:
%F A264379 k=1: a(n) = a(n-2)
%F A264379 k=2: [order 20]
%F A264379 k=3: [order 64]
%F A264379 Empirical for row n:
%F A264379 n=1: a(n) = a(n-1) +a(n-3) +a(n-4)
%F A264379 n=2: [order 10]
%F A264379 n=3: [order 70]
%F A264379 n=4: [order 81] for n>85
%e A264379 Some solutions for n=4 k=4
%e A264379 ..1..2..5..4..9....1..6..5..4..7....1..2..5..6..9....5..2..3..6..7
%e A264379 ..0..7.10..3.14....0.11..2..3.14....0..7.10.11.14....0..1.10..9..4
%e A264379 .11..6.15.16.17...15.16.13..8..9...15..3..4..8.17...11.12.13.14.17
%e A264379 .20..8.18.21.22...10.17.20.21.24...16.21.20.13.24...20..8.22.21.24
%e A264379 .12.13.23.24.19...12.22.23.18.19...12.22.23.18.19...15.16.23.18.19
%Y A264379 Row 1 is A006498(n+1).
%K A264379 nonn,tabl
%O A264379 1,2
%A A264379 _R. H. Hardin_, Nov 12 2015