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

Author

R. H. Hardin, Jan 03 2017

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A001629(n-1).

Column 2 is A279262.

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