A280440 T(n,k)=Number of nXk 0..1 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 0, 1, 4, 1, 2, 10, 10, 2, 5, 20, 21, 20, 5, 10, 38, 42, 42, 38, 10, 20, 68, 77, 80, 77, 68, 20, 38, 120, 136, 138, 138, 136, 120, 38, 71, 208, 236, 232, 225, 232, 236, 208, 71, 130, 358, 404, 386, 360, 360, 386, 404, 358, 130, 235, 612, 687, 640, 574, 548, 574, 640, 687

Offset

1,5

Comments

Table starts

...0...0....1....2....5...10...20...38...71..130...235...420...744..1308..2285

...0...4...10...20...38...68..120..208..358..612..1042..1768..2992..5052..8514

...1..10...21...42...77..136..236..404..687.1162..1959..3294..5528..9262.15497

...2..20...42...80..138..232..386..640.1062.1764..2934..4884..8134.13548.22562

...5..38...77..138..225..360..574..920.1487.2422..3971..6542.10814.17914.29713

..10..68..136..232..360..548..834.1284.2008.3188..5128..8332.13638.22436.37032

..20.120..236..386..574..834.1211.1784.2684.4128..6478.10334.16693.27208.44620

..38.208..404..640..920.1284.1784.2512.3620.5360..8152.12692.20136.32400.52660

..71.358..687.1062.1487.2008.2684.3620.4989.7078.10365.15642.24224.38290.61451

.130.612.1162.1764.2422.3188.4128.5360.7078.9604.13474.19576.29384.45340.71490

Links

R. H. Hardin, Table of n, a(n) for n = 1..568

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4)

k=2: a(n) = 3*a(n-1) -a(n-2) -3*a(n-3) +a(n-4) +a(n-5)

k=3: a(n) = 3*a(n-1) -a(n-2) -3*a(n-3) +a(n-4) +a(n-5) for n>6

k=4: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>7

k=5: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>7

k=6: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>7

k=7: a(n) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>7

Example

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

Crossrefs

Column 1 is A001629(n-1).

Column 2 is A279262.

Sequence in context: A233528 A084604 A152253 * A024569 A206692 A159756

Adjacent sequences: A280437 A280438 A280439 * A280441 A280442 A280443

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 03 2017

Status

approved