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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. 14

%I

%S 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 3778,3249,347,1,40,544,14329,60858,63575,22484,1343,0,64,1357,88264,

%U 711068,1742881,828400,156293,4172,1,104,5100,538417,9407584,45132986,48714516

%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 2,-2 -1,0 -1,2 1,0 or 0,-1.

%C Table starts

%C .1.....2.......4..........6.............9..............15.................25

%C .0.....1.......6..........9............61.............121................544

%C .1....13......80........385..........2345...........14329..............88264

%C .0....25.....441.......3778.........60858..........711068............9407584

%C .1...128....3249......63575.......1742881........45132986.........1187897216

%C .0...347...22484.....828400......48714516......2546661201.......135926940964

%C .1..1343..156293...11888603....1363452981....149731056598.....16353452350876

%C .0..4172.1097881..163298870...38221084820...8620411258657...1906883090233889

%C .1.14711.7657324.2275569624.1068788896516.499872831041401.225710195773223581

%H R. H. Hardin, <a href="/A264379/b264379.txt">Table of n, a(n) for n = 1..144</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-2)

%F k=2: [order 20]

%F k=3: [order 64]

%F Empirical for row n:

%F n=1: a(n) = a(n-1) +a(n-3) +a(n-4)

%F n=2: [order 10]

%F n=3: [order 70]

%F n=4: [order 81] for n>85

%e Some solutions for n=4 k=4

%e ..1..2..5..4..9....1..6..5..4..7....1..2..5..6..9....5..2..3..6..7

%e ..0..7.10..3.14....0.11..2..3.14....0..7.10.11.14....0..1.10..9..4

%e .11..6.15.16.17...15.16.13..8..9...15..3..4..8.17...11.12.13.14.17

%e .20..8.18.21.22...10.17.20.21.24...16.21.20.13.24...20..8.22.21.24

%e .12.13.23.24.19...12.22.23.18.19...12.22.23.18.19...15.16.23.18.19

%Y Row 1 is A006498(n+1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Nov 12 2015

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Last modified August 18 15:00 EDT 2019. Contains 326106 sequences. (Running on oeis4.)