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A264285
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.
13
1, 4, 1, 8, 10, 1, 16, 32, 26, 1, 33, 102, 132, 69, 1, 69, 360, 675, 556, 181, 1, 145, 1228, 4189, 4484, 2324, 476, 1, 300, 4156, 23852, 47492, 29742, 9724, 1252, 1, 624, 14148, 134432, 448821, 537057, 197283, 40692, 3292, 1, 1300, 48188, 768664, 4227024
OFFSET
1,2
COMMENTS
Table starts
.1.....4.......8........16..........33.............69..............145
.1....10......32.......102.........360...........1228.............4156
.1....26.....132.......675........4189..........23852...........134432
.1....69.....556......4484.......47492.........448821..........4227024
.1...181....2324.....29742......537057........8405669........131452948
.1...476....9724....197283.....6080234......157344756.......4076914388
.1..1252...40692...1308629....68815948.....2943284092.....126311779972
.1..3292..170268...8680430...778858184....55051679668....3911932445892
.1..8657..712468..57579243..8815152033..1029653214581..121136137544916
.1.22765.2981244.381936079.99770013733.19257696830753.3750881659750212
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +3*a(n-2) +3*a(n-3) +a(n-4)
k=3: a(n) = 3*a(n-1) +4*a(n-2) +4*a(n-3)
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)
k=5: [order 28]
k=6: [order 36]
k=7: [order 34]
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2) +2*a(n-3) +a(n-4) +a(n-5) -a(n-6)
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
n=3: [order 56]
EXAMPLE
Some solutions for n=4 k=4
..7..0..9..2..3....7..1..9..2..4....0..1..9..2..3....0..1..9..2..3
.12..1..6..8..4....0.13..6..3..8....5.13..6..7..4...12..5.14..7..4
..5.11.19.13.14....5.10.11.12.14...10.11.12..8.14...10..6.11..8.13
.10.23.16.17.18...22.15.16.18.19...22.15.24.17.18...15.23.16.17.19
.15.20.21.22.24...20.21.17.23.24...20.16.21.23.19...20.21.22.18.24
CROSSREFS
Column 2 is A099234(n+1).
Row 1 is A264166.
Sequence in context: A105533 A124848 A090219 * A125129 A324780 A280108
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 10 2015
STATUS
approved