A297993 - OEIS

%I #4 Jan 10 2018 07:37:59

%S 0,1,1,1,4,1,2,17,17,2,3,49,48,49,3,5,166,146,146,166,5,8,573,424,466,

%T 424,573,8,13,1933,1274,1446,1446,1274,1933,13,21,6538,3820,4648,5100,

%U 4648,3820,6538,21,34,22165,11529,14888,18189,18189,14888,11529,22165,34

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 6 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ..0.....1.....1......2......3.......5........8........13.........21.........34

%C ..1.....4....17.....49....166.....573.....1933......6538......22165......75089

%C ..1....17....48....146....424....1274.....3820.....11529......34783.....104826

%C ..2....49...146....466...1446....4648....14888.....47399.....150849.....480015

%C ..3...166...424...1446...5100...18189....62390....213997.....735000....2520806

%C ..5...573..1274...4648..18189...74675...290466...1134198....4475863...17501388

%C ..8..1933..3820..14888..62390..290466..1276012...5745438...26249179..117931466

%C .13..6538.11529..47399.213997.1134198..5745438..30240388..163303980..862771193

%C .21.22165.34783.150849.735000.4475863.26249179.163303980.1056360518.6667346762

%H R. H. Hardin, <a href="/A297993/b297993.txt">Table of n, a(n) for n = 1..364</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1) +a(n-2)

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

%F k=3: [order 11] for n>13

%F k=4: [order 24] for n>27

%F k=5: [order 99] for n>104

%e Some solutions for n=6 k=4

%e ..0..1..1..0. .0..0..0..0. .0..1..0..1. .0..0..0..1. .0..1..1..1

%e ..1..0..1..0. .0..1..1..0. .0..1..0..1. .1..1..1..0. .0..0..0..0

%e ..1..0..1..0. .0..1..1..0. .0..0..0..1. .0..0..0..1. .1..1..1..0

%e ..1..0..1..0. .1..1..1..1. .0..1..0..1. .1..1..1..0. .0..0..1..1

%e ..1..0..1..0. .0..1..1..0. .1..1..0..1. .1..0..0..1. .1..0..0..0

%e ..0..1..0..0. .0..1..1..0. .1..0..0..1. .1..0..1..1. .1..1..1..1

%Y Column 1 is A000045(n-1).

%Y Column 2 is A297817.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jan 10 2018