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A264506 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 -1,1 0,-1 0,1 or 1,0. 14

%I

%S 1,1,2,3,2,3,6,14,4,4,12,38,46,8,6,24,137,211,149,16,9,46,432,1235,

%T 1224,524,32,13,91,1417,6613,11464,7177,1790,64,19,177,4554,35356,

%U 105324,110185,41622,6084,128,28,349,14710,190821,934515,1697577,1041411,241432

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

%C Table starts

%C ..1...1......3........6.........12............24..............46

%C ..2...2.....14.......38........137...........432............1417

%C ..3...4.....46......211.......1235..........6613...........35356

%C ..4...8....149.....1224......11464........105324..........934515

%C ..6..16....524.....7177.....110185.......1697577........24950224

%C ..9..32...1790....41622....1041411......26941396.......655642859

%C .13..64...6084...241432....9813822.....427111736.....17171750212

%C .19.128..20812..1401492...92711566....6776356720....450129538653

%C .28.256..71127..8132167..875322080..107417903076..11788157463588

%C .41.512.242856.47182878.8261489271.1702319756800.308570749630453

%H R. H. Hardin, <a href="/A264506/b264506.txt">Table of n, a(n) for n = 1..179</a>

%F Empirical for column k:

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

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

%F k=3: [order 14]

%F k=4: a(n) = 6*a(n-1) -5*a(n-2) +36*a(n-3) -72*a(n-4) -243*a(n-6) for n>7

%F k=5: [order 84]

%F k=6: [order 36] for n>38

%F Empirical for row n:

%F n=1: a(n) = 2*a(n-1) +a(n-2) -3*a(n-3) +a(n-4) +2*a(n-5) -a(n-6)

%F n=2: [order 14]

%F n=3: [order 69]

%e Some solutions for n=4 k=4

%e ..1..0..3..2..8....1..2..6..4..3....1..2..3..4..8....1..0..3..4..8

%e ..6.10.11..9..4....0.10.11..9..8....0..7.11.12.13....6..7..2..9.13

%e ..5.12..7.14.13....5.12..7.17.13....5..6.16.14..9....5.10.11.14.18

%e .16.20.18.17.23...16.20.18.19.14...10.20.21.19.18...16.20.12.17.23

%e .15.22.21.24.19...15.22.21.24.23...15.22.17.24.23...15.22.21.24.19

%Y Column 1 is A000930(n+1).

%Y Column 2 is A000079(n-1).

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_, Nov 15 2015

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Last modified September 26 16:15 EDT 2021. Contains 347670 sequences. (Running on oeis4.)