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

Author

R. H. Hardin, Jan 25 2016

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 2 is A000079(n-1).

Column 3 is A082685(n-1).

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]