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R. H. Hardin, <a href="/A306166/b306166.txt">Table of n, a(n) for n = 1..287</a>

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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 4, 4, 8, 5, 5, 8, 16, 9, 17, 9, 16, 32, 22, 32, 32, 22, 32, 64, 45, 77, 103, 77, 45, 64, 128, 101, 207, 298, 298, 207, 101, 128, 256, 218, 523, 962, 1188, 962, 523, 218, 256, 512, 477, 1304, 2966, 4849, 4849, 2966, 1304, 477, 512, 1024, 1041, 3307, 8756, 19176

1,2

Table starts

...1...2....4.....8.....16......32.......64.......128........256.........512

...2...4....5.....9.....22......45......101.......218........477........1041

...4...5...17....32.....77.....207......523......1304.......3307........8414

...8...9...32...103....298.....962.....2966......8756......26287.......79873

..16..22...77...298...1188....4849....19176.....75681.....302442.....1206813

..32..45..207...962...4849...25226...128710....660871....3402775....17536734

..64.101..523..2966..19176..128710...842280...5553315...36528087...240890311

.128.218.1304..8756..75681..660871..5553315..47632142..405555135..3465256979

.256.477.3307.26287.302442.3402775.36528087.405555135.4469582265.49440451905

Empirical for column k:

k=1: a(n) = 2*a(n-1)

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

k=3: a(n) = a(n-1) +2*a(n-2) +5*a(n-3) +2*a(n-4) -2*a(n-5) -8*a(n-6) -8*a(n-7) for n>10

k=4: [order 18] for n>23

k=5: [order 40] for n>47

Some solutions for n=5 k=4

..0..0..0..0. .0..1..0..0. .0..0..0..1. .0..0..0..0. .0..0..1..1

..1..0..0..0. .0..0..0..1. .1..0..1..0. .0..0..0..1. .0..0..1..1

..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .1..1..1..1

..1..0..0..0. .1..0..1..0. .0..0..0..0. .1..0..0..0. .1..1..1..1

..0..0..0..0. .0..0..0..1. .0..1..0..0. .0..0..0..0. .1..0..1..1

Column 1 is A000079(n-1).

Column 2 is A052962 for n>2.

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nonn,tabl

R. H. Hardin, Jun 23 2018

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