A317759 -id:A317759 - cp's OEIS frontend

A318075 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 6, 4, 8, 10, 10, 8, 16, 20, 18, 20, 16, 32, 42, 41, 41, 42, 32, 64, 89, 81, 73, 81, 89, 64, 128, 190, 179, 149, 149, 179, 190, 128, 256, 407, 404, 372, 316, 372, 404, 407, 256, 512, 873, 893, 861, 854, 854, 861, 893, 873, 512, 1024, 1874, 2000, 2016, 2195

Offset: 1

R. H. Hardin, Aug 15 2018

Table starts
...1...2....4....8....16.....32.....64.....128......256.......512.......1024
...2...6...10...20....42.....89....190.....407......873......1874.......4024
...4..10...18...41....81....179....404.....893.....2000......4516......10125
...8..20...41...73...149....372....861....2016.....4901.....11698......27986
..16..42...81..149...316....854...2195....5752....15565.....41364.....110930
..32..89..179..372...854...3029...9966...31057...102906....339938....1115341
..64.190..404..861..2195...9966..46884..184156...819263...3703730...15865269
.128.407..893.2016..5752..31057.184156..935951..5311510..30435406..167286074
.256.873.2000.4901.15565.102906.819263.5311510.38183961.285095330.2029620744

			Some solutions for n=5 k=4
..0..1..1..0. .0..0..0..1. .0..0..0..0. .0..0..1..1. .0..1..1..0
..1..1..0..1. .0..0..1..0. .0..1..1..0. .0..0..1..1. .1..1..0..0
..1..1..1..1. .0..0..0..0. .0..0..0..0. .0..0..1..1. .1..0..0..0
..1..1..1..1. .0..1..0..0. .0..0..0..1. .0..0..1..1. .0..0..0..0
..1..1..1..0. .1..0..0..1. .0..0..1..1. .0..0..1..1. .1..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..420

Column 1 is A000079(n-1).

Column 2 is A317759.

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -a(n-4) for n>6
k=3: a(n) = 2*a(n-1) +a(n-2) +a(n-3) -3*a(n-4) -6*a(n-5) +6*a(n-6) for n>10
k=4: [order 18] for n>21
k=5: [order 29] for n>33
k=6: [order 56] for n>61

A318343 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 2, 2, 4, 6, 4, 8, 10, 10, 8, 16, 20, 20, 20, 16, 32, 42, 36, 36, 42, 32, 64, 89, 76, 67, 76, 89, 64, 128, 190, 160, 148, 148, 160, 190, 128, 256, 407, 344, 343, 393, 343, 344, 407, 256, 512, 873, 748, 817, 1115, 1115, 817, 748, 873, 512, 1024, 1874, 1624, 1975, 3321

Offset: 1

R. H. Hardin, Aug 24 2018

Table starts
...1...2....4....8....16.....32......64......128.......256........512
...2...6...10...20....42.....89.....190......407.......873.......1874
...4..10...20...36....76....160.....344......748......1624.......3544
...8..20...36...67...148....343.....817.....1975......4788......11644
..16..42...76..148...393...1115....3321....10111.....30943......95244
..32..89..160..343..1115...4133...16267....66070....270320....1112195
..64.190..344..817..3321..16267...86487...476348...2647555...14797928
.128.407..748.1975.10111..66070..476348..3590263..27322989..209259065
.256.873.1624.4788.30943.270320.2647555.27322989.285034170.2994059337

			Some solutions for n=5 k=4
..0..1..1..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
..1..1..0..0. .1..1..1..1. .0..1..0..0. .0..0..0..0. .1..1..1..1
..1..0..0..1. .1..1..1..0. .0..0..1..0. .1..1..1..1. .1..1..1..1
..0..0..1..1. .1..1..0..0. .0..0..0..0. .1..1..1..0. .1..1..1..0
..0..1..1..0. .1..0..0..1. .0..0..0..1. .1..1..0..0. .1..1..0..0

R. H. Hardin, Table of n, a(n) for n = 1..611

Column 1 is A000079(n-1).

Column 2 is A317759.

Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) -a(n-3) -a(n-4) for n>6
k=3: a(n) = 2*a(n-1) +2*a(n-2) -3*a(n-3) -2*a(n-4) +2*a(n-5) for n>6
k=4: [order 8] for n>9
k=5: [order 15] for n>18
k=6: [order 23] for n>27
k=7: [order 36] for n>41

cp's OEIS Frontend

A318075 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

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