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A264569 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 1,0 1,1 0,-1 or -1,1.

%I A264569 #4 Nov 17 2015 19:12:29
%S A264569 1,1,1,1,2,1,2,4,4,2,2,8,10,8,2,4,24,44,31,16,3,4,64,143,192,79,32,4,
%T A264569 7,160,633,1130,888,224,64,5,9,384,2172,8356,7808,4104,646,128,7,13,
%U A264569 960,8409,47571,96429,57265,18540,1784,256,9,18,2432,32046,305844,868613
%N A264569 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 1,0 1,1 0,-1 or -1,1.
%C A264569 Table starts
%C A264569 .1...1.....1.......2.........2...........4.............4...............7
%C A264569 .1...2.....4.......8........24..........64...........160.............384
%C A264569 .1...4....10......44.......143.........633..........2172............8409
%C A264569 .2...8....31.....192......1130........8356.........47571..........305844
%C A264569 .2..16....79.....888......7808.......96429........868613.........8968735
%C A264569 .3..32...224....4104.....57265.....1133040......16284544.......273793368
%C A264569 .4..64...646...18540....403872....13182464.....298587595......8004883334
%C A264569 .5.128..1784...85752...2873739...152082304....5442431797....235814997396
%C A264569 .7.256..5010..389340..20432891..1755041376...99386232806...6882481295560
%C A264569 .9.512.14026.1787832.144677017.20212718576.1803702025944.200087118615516
%H A264569 R. H. Hardin, <a href="/A264569/b264569.txt">Table of n, a(n) for n = 1..179</a>
%F A264569 Empirical for column k:
%F A264569 k=1: a(n) = a(n-2) +a(n-3)
%F A264569 k=2: a(n) = 2*a(n-1)
%F A264569 k=3: [order 15]
%F A264569 k=4: a(n) = 18*a(n-2) +36*a(n-3) -45*a(n-4) -216*a(n-5) -243*a(n-6) for n>7
%F A264569 k=5: [order 84]
%F A264569 k=6: [order 36] for n>40
%F A264569 Empirical for row n:
%F A264569 n=1: a(n) = a(n-2) +a(n-3) +a(n-4) -a(n-6)
%F A264569 n=2: a(n) = 2*a(n-1) +8*a(n-4)
%F A264569 n=3: [order 70]
%F A264569 n=4: [order 56]
%e A264569 Some solutions for n=4 k=4
%e A264569 ..1..2..3..4..8....1..5..6..4..8....1..5..3..4..8....1..2..3..4..8
%e A264569 ..0..7.11..9.13....0..7..2..9..3....0..7..2..9.13....0.10.11.12.13
%e A264569 ..5..6.16.17.18...11.15.16.17.18...11..6.16.17.18....5..6..7.14..9
%e A264569 .10.20.21.12.14...10.20.12.13.14...10.20.21.12.14...16.20.21.19.23
%e A264569 .15.22.23.24.19...21.22.23.24.19...15.22.23.24.19...15.22.17.24.18
%Y A264569 Column 1 is A000931(n+4).
%Y A264569 Column 2 is A000079(n-1).
%Y A264569 Row 1 is A253412(n-2).
%K A264569 nonn,tabl
%O A264569 1,5
%A A264569 _R. H. Hardin_, Nov 17 2015