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A264534
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 -2,-2 -1,0 0,1 or 1,0.
13
1, 1, 0, 1, 4, 1, 1, 2, 4, 0, 1, 1, 13, 19, 1, 1, 16, 29, 40, 49, 0, 1, 16, 89, 166, 229, 100, 1, 1, 16, 261, 824, 1424, 696, 316, 0, 1, 68, 673, 3256, 13144, 8180, 3273, 766, 1, 1, 97, 1949, 15028, 82961, 119810, 59259, 12832, 1883, 0, 1, 128, 5545, 64156, 634896, 1293264
OFFSET
1,5
COMMENTS
Table starts
.1....1......1........1..........1............1............1............1
.0....4......2........1.........16...........16...........16...........68
.1....4.....13.......29.........89..........261..........673.........1949
.0...19.....40......166........824.........3256........15028........64156
.1...49....229.....1424......13144........82961.......634896......4694020
.0..100....696.....8180.....119810......1293264.....15187422....179414540
.1..316...3273....59259....1270837.....22000750....434877820...7956766442
.0..766..12832...373106...14103392....400032412..12164306720.370349399305
.1.1883..52897..2412437..139422769...6346673554.324326909569
.0.5221.209890.15444786.1489609039.110239970880
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-2)
k=2: [order 20]
k=3: [order 42]
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = 4*a(n-3) +2*a(n-4) +2*a(n-5) -2*a(n-9) -a(n-10)
n=3: a(n) = a(n-1) +12*a(n-3) +16*a(n-5)
n=4: [order 10] for n>11
EXAMPLE
Some solutions for n=4 k=4
.12..6.14..2..3...12.13.14..2..3....5..6..7..8..9...12.13..1..2..3
..0..1.19..7..4....0..1..6..7..4....0..1..2..3..4....0.11..6..7..4
..5.10.17..8..9....5.16.11..8..9...22.23.24.12.13....5.10.24..8..9
.20.11.22.13.24...10.21.22.23.24...10.11.16.17.14...20.21.22.23.14
.15.16.21.18.23...15.20.17.18.19...15.20.21.18.19...15.16.17.18.19
CROSSREFS
Sequence in context: A030747 A222171 A325529 * A228489 A096103 A204456
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 17 2015
STATUS
approved