A259770 - OEIS

%I #4 Jul 04 2015 21:41:59

%S 32,49,49,104,87,104,201,167,167,201,376,299,256,299,376,745,564,385,

%T 385,564,745,1494,1086,612,451,612,1086,1494,2897,2045,1108,474,474,

%U 1108,2045,2897,5610,3870,1708,835,400,835,1708,3870,5610,11065,7371,2700,872

%N T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00000001 or 00000101

%C Table starts

%C ....32....49..104..201.376..745.1494.2897.5610.11065.21780.42461.82984.162977

%C ....49....87..167..299.564.1086.2045.3870.7371.14001.26647.50766.96574.183815

%C ...104...167..256..385.612.1108.1708.2700.4660..7378.11350.19232.31280..48032

%C ...201...299..385..451.474..835..872..968.1532..1794..2116..2746..4218...4546

%C ...376...564..612..474.400..798..524..450..588...644...540...568..1060....716

%C ...745..1086.1108..835.798.1805..654..436..544...634...528...688..1512....478

%C ..1494..2045.1708..872.524..654..480..392..492...536...424...420...532....402

%C ..2897..3870.2700..968.450..436..392..336..368...428...404...410...430....416

%C ..5610..7371.4660.1532.588..544..492..368..384...362...456...404...404....424

%C .11065.14001.7378.1794.644..634..536..428..362...368...438...398...404....366

%H R. H. Hardin, <a href="/A259770/b259770.txt">Table of n, a(n) for n = 1..1248</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-2) +2*a(n-3) +6*a(n-4) +2*a(n-5) -a(n-6) +2*a(n-7) -a(n-8) for n>9

%F k=2: [order 11] for n>12

%F k=3: [order 14] for n>17

%F k=4: a(n) = 3*a(n-7) +5*a(n-10) +a(n-13) -a(n-14) -a(n-17) -2*a(n-21) for n>24

%F k=5: a(n) = 2*a(n-7) -2*a(n-21) +a(n-28) for n>34

%F k=6: a(n) = a(n-14) for n>21

%F k=7: a(n) = a(n-1) -a(n-2) +a(n-3) -a(n-4) +a(n-5) -a(n-6) +a(n-7) -a(n-8) +a(n-9) -a(n-10) +a(n-11) -a(n-12) +a(n-13) for n>20

%F Empirical periodic continuations for column k:

%F k=6: period of length 14 starting at n=8: 436 544 634 528 688 1512 478 442 570 726 674 764 1724 590

%F k=7: period of length 14 starting at n=8: 392 492 536 424 420 532 402 344 420 500 416 412 566 448

%e Some solutions for n=4 k=4

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

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jul 04 2015