A264299 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 0,1 0,-2 1,0 or -1,0.

1, 2, 0, 5, 9, 1, 10, 8, 20, 0, 16, 24, 89, 56, 1, 29, 177, 332, 192, 169, 0, 61, 288, 1952, 1672, 1413, 441, 1, 117, 944, 10449, 25080, 14881, 4352, 1258, 0, 212, 4209, 51825, 146688, 297721, 94320, 24781, 3520, 1, 401, 9944, 271385, 1346944, 3890569

Offset

1,2

Comments

Table starts

.1.....2.......5........10.........16..........29..........61.........117

.0.....9.......8........24........177.........288.........944........4209

.1....20......89.......332.......1952.......10449.......51825......271385

.0....56.....192......1672......25080......146688.....1346944....13834555

.1...169....1413.....14881.....297721.....3890569....53407877...839565293

.0...441....4352.....94320....3654505....66462504..1659712320.45752436553

.1..1258...24781....727970...44552352..1510247849.59343473405

.0..3520...90112...5007568..542471200.28497437872

.1..9701..449665..36810037.6626768169

.0.27216.1781256.260065872

Links

R. H. Hardin, Table of n, a(n) for n = 1..97

Formula

Empirical for column k:

k=1: a(n) = a(n-2)

k=2: a(n) = a(n-1) +4*a(n-2) +5*a(n-3) -5*a(n-4) -5*a(n-5) +4*a(n-6) -a(n-7) -a(n-8)

k=3: [order 21]

Empirical for row n:

n=1: a(n) = a(n-1) +3*a(n-3) +a(n-4) +a(n-5) -3*a(n-6) -2*a(n-7) +a(n-9)

n=2: [order 35]

Example

Some solutions for n=4 k=4
..5..0..1..2..9....5..0..4..2..9....5..0..4..8..9....2..0..1..8..9
.10.11..6..3..4....7..1..6..3..8...10..1..2..3.14....7.11..6..3..4
.15.16..7..8.19...15.10.14.12.13...12..6..7.18.13....5.16.14.18.13
.17.21.12.13.14...20.11.16.17.24...20.11.19.17.24...10.21.12.23.24
.22.20.24.18.23...22.23.21.18.19...15.16.21.22.23...15.20.17.22.19

Crossrefs

Sequence in context: A192883 A011435 A139309 * A374063 A243445 A227569

Adjacent sequences: A264296 A264297 A264298 * A264300 A264301 A264302

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 11 2015

Status

approved