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

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

R. H. Hardin, Table of n, a(n) for n = 1..140

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

Adjacent sequences: A215785 A215786 A215787 * A215789 A215790 A215791

Keyword

nonn,tabl

Author

R. H. Hardin Aug 23 2012

Status

approved