A268079 T(n,k)=Number of nXk nonnegative integer arrays with new values introduced in each row and column in sequential order starting with zero.

1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 8, 18, 8, 1, 1, 16, 86, 86, 16, 1, 1, 32, 422, 1094, 422, 32, 1, 1, 64, 2094, 15106, 15106, 2094, 64, 1, 1, 128, 10438, 216734, 637358, 216734, 10438, 128, 1, 1, 256, 52126, 3168306, 29309170, 29309170, 3168306, 52126, 256, 1, 1, 512

Offset

1,5

Comments

Table starts

.1...1......1.........1.............1.................1.....................1

.1...2......4.........8............16................32....................64

.1...4.....18........86...........422..............2094.................10438

.1...8.....86......1094.........15106............216734...............3168306

.1..16....422.....15106........637358..........29309170............1412290158

.1..32...2094....216734......29309170........4617638834..........795460720710

.1..64..10438...3168306....1412290158......795460720710.......517992936833258

.1.128..52126..46777214...69903748498...144635795908942....369867566612849678

.1.256.260502.694585586.3516426536462.27199854725237562.280350778114908738774

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

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

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

k=3: a(n) = 7*a(n-1) -10*a(n-2)

k=4: a(n) = 36*a(n-1) -463*a(n-2) +2640*a(n-3) -6700*a(n-4) +6000*a(n-5)

k=5: [order 14]

k=6: [order 45]

Example

Some solutions for n=4 k=4
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..1..0..1....0..0..0..0....0..1..0..1....0..1..1..0....0..0..1..0
..0..1..1..1....0..1..1..1....0..0..1..2....0..0..1..0....0..0..1..1
..0..0..1..2....0..1..2..1....0..1..1..0....0..1..0..0....0..0..0..1

Crossrefs

Column 2 is A000079(n-1).

Column 3 is A082685(n-1).

Sequence in context: A331406 A034372 A268056 * A202549 A155971 A176480

Adjacent sequences: A268076 A268077 A268078 * A268080 A268081 A268082

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 25 2016

Status

approved