A279262 -id:A279262 - cp's OEIS frontend

A281765 T(n,k)=Number of nXk 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 0, 2, 4, 0, 2, 14, 10, 0, 5, 40, 47, 20, 0, 8, 110, 152, 90, 38, 0, 15, 280, 609, 560, 201, 68, 0, 26, 698, 2138, 2808, 1872, 374, 120, 0, 46, 1696, 7466, 13968, 12191, 5948, 672, 208, 0, 80, 4052, 25798, 68362, 85844, 49986, 18358, 1172, 358, 0, 139, 9564, 87397

Offset: 1

R. H. Hardin, Jan 29 2017

Table starts
.0...0....2......2........5.........8..........15...........26.............46
.0...4...14.....40......110.......280.........698.........1696...........4052
.0..10...47....152......609......2138........7466........25798..........87397
.0..20...90....560.....2808.....13968.......68362.......323280........1529974
.0..38..201...1872....12191.....85844......589990......3845590.......25703392
.0..68..374...5948....49986....502276.....4845178.....43943360......414035752
.0.120..672..18358...201450...2848436....38998648....491290688.....6531040026
.0.208.1172..55048...795220..15817652...306847534...5380228500...100838834642
.0.358.2015.162120..3098932..86332266..2376142873..58064622712..1533079336619
.0.612.3442.471340.11944444.465260812.18172170592.619082149716.23019093115418

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

R. H. Hardin, Table of n, a(n) for n = 1..180

Column 2 is A279262.

Row 1 is A006367(n-1).

Empirical for column k:
k=1: a(n) = a(n-1)
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) = 4*a(n-1) -4*a(n-2) -2*a(n-3) +4*a(n-4) -a(n-6) for n>11
k=4: [order 29] for n>32
k=5: [order 48] for n>57
Empirical for row n:
n=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4) for n>5
n=2: [order 9]
n=3: [order 40] for n>41

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.

Original entry on oeis.org

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

R. H. Hardin, Jan 03 2017

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

			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

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

Column 1 is A001629(n-1).

Column 2 is A279262.

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

cp's OEIS Frontend

A281765 T(n,k)=Number of nXk 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

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