A264299 - OEIS

%I #4 Nov 11 2015 07:40:02

%S 1,2,0,5,9,1,10,8,20,0,16,24,89,56,1,29,177,332,192,169,0,61,288,1952,

%T 1672,1413,441,1,117,944,10449,25080,14881,4352,1258,0,212,4209,51825,

%U 146688,297721,94320,24781,3520,1,401,9944,271385,1346944,3890569

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

%C Table starts

%C .1.....2.......5........10.........16..........29..........61.........117

%C .0.....9.......8........24........177.........288.........944........4209

%C .1....20......89.......332.......1952.......10449.......51825......271385

%C .0....56.....192......1672......25080......146688.....1346944....13834555

%C .1...169....1413.....14881.....297721.....3890569....53407877...839565293

%C .0...441....4352.....94320....3654505....66462504..1659712320.45752436553

%C .1..1258...24781....727970...44552352..1510247849.59343473405

%C .0..3520...90112...5007568..542471200.28497437872

%C .1..9701..449665..36810037.6626768169

%C .0.27216.1781256.260065872

%H R. H. Hardin, <a href="/A264299/b264299.txt">Table of n, a(n) for n = 1..97</a>

%F Empirical for column k:

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

%F k=2: a(n) = a(n-1) +4*a(n-2) +5*a(n-3) -5*a(n-4) -5*a(n-5) +4*a(n-6) -a(n-7) -a(n-8)

%F k=3: [order 21]

%F Empirical for row n:

%F n=1: a(n) = a(n-1) +3*a(n-3) +a(n-4) +a(n-5) -3*a(n-6) -2*a(n-7) +a(n-9)

%F n=2: [order 35]

%e Some solutions for n=4 k=4

%e ..5..0..1..2..9....5..0..4..2..9....5..0..4..8..9....2..0..1..8..9

%e .10.11..6..3..4....7..1..6..3..8...10..1..2..3.14....7.11..6..3..4

%e .15.16..7..8.19...15.10.14.12.13...12..6..7.18.13....5.16.14.18.13

%e .17.21.12.13.14...20.11.16.17.24...20.11.19.17.24...10.21.12.23.24

%e .22.20.24.18.23...22.23.21.18.19...15.16.21.22.23...15.20.17.22.19

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Nov 11 2015