A264476 - OEIS

%I #9 Nov 15 2015 07:34:00

%S 0,1,1,0,2,0,0,4,4,1,1,8,6,8,1,0,17,16,16,16,1,0,36,57,120,49,32,2,1,

%T 76,160,456,456,124,64,2,0,160,484,2272,3540,2232,384,128,3,0,337,

%U 1449,11044,28489,24773,10116,1041,256,4,1,710,4250,49200,215607,310748

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

%C Table starts

%C .0...1....0......0........1..........0............0..............1

%C .1...2....4......8.......17.........36...........76............160

%C .0...4....6.....16.......57........160..........484...........1449

%C .1...8...16....120......456.......2272........11044..........49200

%C .1..16...49....456.....3540......28489.......215607........1711113

%C .1..32..124...2232....24773.....310748......4039259.......50217832

%C .2..64..384..10116...174927....3842048.....74367790.....1462247321

%C .2.128.1041..45792..1262270...43644384...1358980008....44706530288

%C .3.256.2868.212112..8905776..505769648..25131223920..1299344783466

%C .4.512.8189.960336.63373156.5849013488.454913826610.38128043682868

%H R. H. Hardin, <a href="/A264476/b264476.txt">Table of n, a(n) for n = 1..220</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-2) +a(n-3)

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

%F k=3: [order 15]

%F 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 k=5: [order 84] for n>86

%F k=6: [order 36] for n>40

%F Empirical for row n:

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

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

%F n=3: [order 15]

%F n=4: [order 10] for n>11

%F n=5: [order 84]

%e Some solutions for n=4 k=4

%e ..6..0..1..9..3....6..0..1..2..3....6..7..8..9..3....6..7..8..2..3

%e .11..5..2..7..4...11.12.13.14..4....0..1..2.14..4....0..1.13.14..4

%e .16.10.18..8.13....5.10..7.19..9...16.10.11.19.13...16.17.11.12..9

%e .21.22.23.24.14...21.22.16.24..8...21..5.12.24.18...10..5.23.24.18

%e .15.20.17.12.19...15.20.17.18.23...15.20.17.22.23...15.20.21.22.19

%Y Column 1 is A000931(n+1).

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

%Y Row 2 is A008999(n-1).

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Nov 14 2015