A260015 - OEIS

%I #4 Jul 13 2015 08:48:52

%S 36,49,49,109,98,109,209,252,252,209,436,578,889,578,436,828,1232,

%T 2492,2492,1232,828,1744,2738,6944,8450,6944,2738,1744,3344,6262,

%U 18356,25600,25600,18356,6262,3344,7005,14112,56137,84050,87024,84050,56137,14112

%N T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with each 3X3 subblock having clockwise perimeter pattern 00000101 00010101 or 01010101

%C Table starts

%C ....36....49.....109......209......436.......828.......1744........3344

%C ....49....98.....252......578.....1232......2738.......6262.......14112

%C ...109...252.....889.....2492.....6944.....18356......56137......155304

%C ...209...578....2492.....8450....25600.....84050.....292422......985608

%C ...436..1232....6944....25600....87024....294336....1231648.....4380288

%C ...828..2738...18356....84050...294336...1210568....5674360....24724512

%C ..1744..6262...56137...292422..1231648...5674360...33390411...166527544

%C ..3344.14112..155304...985608..4380288..24724512..166527544..1002982472

%C ..7005.31500..457083..3251280.16773440.101249348..840032861..5561958496

%C .13424.70688.1237656.10857800.58243968.428893472.4030790792.32495162312

%H R. H. Hardin, <a href="/A260015/b260015.txt">Table of n, a(n) for n = 1..880</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-2) +7*a(n-4) +a(n-5) +2*a(n-6) +a(n-7) -a(n-8) +a(n-9) for n>10

%F k=2: a(n) = 2*a(n-1) +a(n-3) +3*a(n-4) -5*a(n-5) -a(n-6) -a(n-8) +a(n-9) for n>10

%F k=3: a(n) = 4*a(n-2) +37*a(n-4) -13*a(n-6) -124*a(n-8) +12*a(n-10) +72*a(n-12) for n>13

%F k=4: [order 16] for n>17

%F k=5: [order 18] for n>21

%F k=6: [order 36] for n>37

%F k=7: [order 56] for n>57

%e Some solutions for n=4 k=4

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

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jul 13 2015