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T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00000001 or 00000011
9

%I #4 Jul 03 2015 19:48:20

%S 32,54,54,140,95,140,242,228,228,242,312,392,568,392,312,722,556,1064,

%T 1064,556,722,1388,1219,1244,2059,1244,1219,1388,1974,2330,2858,2218,

%U 2218,2858,2330,1974,3824,3544,6092,5458,3120,5458,6092,3544,3824,7718

%N T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00000001 or 00000011

%C Table starts

%C ...32....54...140...242...312....722...1388...1974....3824....7718...12060

%C ...54....95...228...392...556...1219...2330...3544....6772...13549...22196

%C ..140...228...568..1064..1244...2858...6092...8638...15640...34858...57256

%C ..242...392..1064..2059..2218...5458..12198..16269...30246...71722..114938

%C ..312...556..1244..2218..3120...7076..13920..21398...42208...89194..149000

%C ..722..1219..2858..5458..7076..16294..33846..51254...99106..219106..370024

%C .1388..2330..6092.12198.13920..33846..75200.109360..207144..488034..830840

%C .1974..3544..8638.16269.21398..51254.109360.165976..330522..758812.1302892

%C .3824..6772.15640.30246.42208..99106.207144.330522..671824.1508650.2625348

%C .7718.13549.34858.71722.89194.219106.488034.758812.1508650.3555562.6283494

%H R. H. Hardin, <a href="/A259723/b259723.txt">Table of n, a(n) for n = 1..612</a>

%F Empirical for column k:

%F k=1: a(n) = 4*a(n-3) +3*a(n-4)

%F k=2: [order 10]

%F k=3: [order 16]

%F k=4: [order 22]

%F k=5: [order 52]

%F k=6: [order 84] for n>85

%e Some solutions for n=4 k=4

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

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jul 03 2015