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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. 6
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified August 17 05:07 EDT 2022. Contains 356184 sequences. (Running on oeis4.)