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

1,5

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......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

Links

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

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) +206208420*a(n-5) -255602200*a(n-6)

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..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

Crossrefs

Column 2 is A000079(n-1).

Column 3 is A082685(n-1).

Sequence in context: A144324 A331406 A034372 * A268079 A202549 A155971

Adjacent sequences: A268053 A268054 A268055 * A268057 A268058 A268059

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 25 2016

Status

approved