login
A215788
T(n,k)=Number of permutations of 0..floor((n*k-1)/2) on even squares of an nXk array such that each row, column, diagonal and (downwards) antidiagonal of even squares is increasing
11
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 5, 2, 1, 1, 1, 1, 5, 12, 10, 4, 1, 1, 1, 1, 5, 42, 29, 25, 4, 1, 1, 1, 1, 14, 110, 262, 189, 50, 8, 1, 1, 1, 1, 14, 462, 932, 2465, 458, 125, 8, 1, 1, 1, 1, 42, 1274, 11694, 26451, 15485, 2988, 250, 16, 1, 1, 1, 1, 42, 6006
OFFSET
1,17
COMMENTS
Table starts
.1.1.1..1....1......1........1..........1...........1...........1...........1
.1.1.1..1....2......2........5..........5..........14..........14..........42
.1.1.1..2....5.....12.......42........110.........462........1274........6006
.1.1.1..2...10.....29......262........932.......11694.......46988......727846
.1.1.1..4...25....189.....2465......26451......530429.....7027942...187205626
.1.1.1..4...50....458....15485.....234217....14296434...297246092.26970790176
.1.1.1..8..125...2988...146205....6812794...673507749.48337803306
.1.1.1..8..250...7241...918637...60485308.18255280444
.1.1.1.16..625..47241..8674386.1761748159
.1.1.1.16.1250.114482.54503318
.1.1.1.32.3125.746892
.1.1.1.32.6250
LINKS
FORMULA
Empirical for column k:
k=4: a(n) = 2*a(n-2)
k=5: a(n) = 5*a(n-2)
k=6: a(n) = 16*a(n-2) -3*a(n-4)
k=7: a(n) = 61*a(n-2) -99*a(n-4) -2*a(n-6)
k=8: a(n) = 272*a(n-2) -3439*a(n-4) -3336*a(n-6) +140*a(n-8)
k=9: a(n) = 1385*a(n-2) -131648*a(n-4) -318070*a(n-6) -4160916*a(n-8) -1097892*a(n-10) +648*a(n-12)
EXAMPLE
Some solutions for n=7 k=4
..0..x..1..x....0..x..1..x....0..x..1..x....0..x..1..x....0..x..1..x
..x..2..x..3....x..2..x..4....x..2..x..4....x..2..x..3....x..2..x..3
..4..x..5..x....3..x..5..x....3..x..5..x....4..x..5..x....4..x..5..x
..x..6..x..8....x..6..x..8....x..6..x..8....x..6..x..7....x..6..x..7
..7..x..9..x....7..x..9..x....7..x..9..x....8..x..9..x....8..x..9..x
..x.10..x.12....x.10..x.12....x.10..x.11....x.10..x.12....x.10..x.11
.11..x.13..x...11..x.13..x...12..x.13..x...11..x.13..x...12..x.13..x
CROSSREFS
Column 5 is A026383(n-1)
Row 2 is A000108(floor((n-1)/2))
Odd squares: A215870
Sequence in context: A157896 A358469 A156072 * A060990 A276309 A165031
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Aug 23 2012
STATUS
approved