A264285 - OEIS

%I #4 Nov 10 2015 14:56:25

%S 1,4,1,8,10,1,16,32,26,1,33,102,132,69,1,69,360,675,556,181,1,145,

%T 1228,4189,4484,2324,476,1,300,4156,23852,47492,29742,9724,1252,1,624,

%U 14148,134432,448821,537057,197283,40692,3292,1,1300,48188,768664,4227024

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

%C Table starts

%C .1.....4.......8........16..........33.............69..............145

%C .1....10......32.......102.........360...........1228.............4156

%C .1....26.....132.......675........4189..........23852...........134432

%C .1....69.....556......4484.......47492.........448821..........4227024

%C .1...181....2324.....29742......537057........8405669........131452948

%C .1...476....9724....197283.....6080234......157344756.......4076914388

%C .1..1252...40692...1308629....68815948.....2943284092.....126311779972

%C .1..3292..170268...8680430...778858184....55051679668....3911932445892

%C .1..8657..712468..57579243..8815152033..1029653214581..121136137544916

%C .1.22765.2981244.381936079.99770013733.19257696830753.3750881659750212

%H R. H. Hardin, <a href="/A264285/b264285.txt">Table of n, a(n) for n = 1..161</a>

%F Empirical for column k:

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

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

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

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

%F k=5: [order 28]

%F k=6: [order 36]

%F k=7: [order 34]

%F Empirical for row n:

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

%F n=2: a(n) = a(n-1) +4*a(n-2) +10*a(n-3) +12*a(n-4) +8*a(n-5) for n>7

%F n=3: [order 56]

%e Some solutions for n=4 k=4

%e ..7..0..9..2..3....7..1..9..2..4....0..1..9..2..3....0..1..9..2..3

%e .12..1..6..8..4....0.13..6..3..8....5.13..6..7..4...12..5.14..7..4

%e ..5.11.19.13.14....5.10.11.12.14...10.11.12..8.14...10..6.11..8.13

%e .10.23.16.17.18...22.15.16.18.19...22.15.24.17.18...15.23.16.17.19

%e .15.20.21.22.24...20.21.17.23.24...20.16.21.23.19...20.21.22.18.24

%Y Column 2 is A099234(n+1).

%Y Row 1 is A264166.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Nov 10 2015