A268056 T(n,k)=Number of nXk 0..2 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, 1082, 422, 32, 1, 1, 64, 2094, 14554, 14554, 2094, 64, 1, 1, 128, 10438, 200818, 560778, 200818, 10438, 128, 1, 1, 256, 52126, 2796826, 22501266, 22501266, 2796826, 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......1082.........14554...........200818..............2796826

.1..16....422.....14554........560778.........22501266............915745002

.1..32...2094....200818......22501266.......2666449962.........322124540754

.1..64..10438...2796826.....915745002.....322124540754......116124404018058

.1.128..52126..39082562...37450557314...39169337042938....42209510913723266

.1.256.260502.546791114.1534144563898.4773343640706306.15385058360607977882

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..0....0..1..1..0....0..0..1..1....0..1..0..0....0..1..1..1
..0..1..0..0....0..1..1..0....0..1..1..2....0..0..0..0....0..1..1..2
..0..1..0..1....0..0..0..0....0..1..1..2....0..0..0..1....0..1..1..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..760

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) = 21*a(n-1) -108*a(n-2) +140*a(n-3)

k=5: a(n) = 62*a(n-1) -969*a(n-2) +4568*a(n-3) -5740*a(n-4)

k=6: a(n) = 184*a(n-1) -8533*a(n-2) +122786*a(n-3) -563036*a(n-4) +700280*a(n-5)

k=7: a(n) = 549*a(n-1) -75693*a(n-2) +3237331*a(n-3) -45379926*a(n-4) [phone]*a(n-5) -255602200*a(n-6)