A230661 - OEIS

%I #4 Oct 27 2013 07:59:01

%S 1,0,0,0,3,0,0,3,3,0,0,9,15,9,0,0,15,21,21,15,0,0,33,135,123,135,33,0,

%T 0,63,177,531,531,177,63,0,0,129,1155,2547,8613,2547,1155,129,0,0,255,

%U 1509,11745,28161,28161,11745,1509,255,0,0,513,9855,54957,477279,337977

%N T(n,k)=Number of nXk 0..2 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j)

%C Table starts

%C .1...0....0.....0.......0........0..........0...........0.............0

%C .0...3....3.....9......15.......33.........63.........129...........255

%C .0...3...15....21.....135......177.......1155........1509..........9855

%C .0...9...21...123.....531.....2547......11745.......54957........255753

%C .0..15..135...531....8613....28161.....477279.....1539207......26178201

%C .0..33..177..2547...28161...337977....3951657....46564959.....547445439

%C .0..63.1155.11745..477279..3951657..169006665..1374288243...59075291211

%C .0.129.1509.54957.1539207.46564959.1374288243.40860127671.1212230763441

%H R. H. Hardin, <a href="/A230661/b230661.txt">Table of n, a(n) for n = 1..312</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1) for n>1

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

%F k=3: a(n) = 9*a(n-2) -4*a(n-4)

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

%F k=5: a(n) = 59*a(n-2) -230*a(n-4) -2*a(n-6) +32*a(n-8) for n>10

%F k=6: [order 23] for n>24

%F k=7: [order 46] for n>47

%e Some solutions for n=5 k=4

%e ..x..0..x..1....x..1..x..0....x..2..x..2....x..2..x..1....x..2..x..2

%e ..2..x..1..x....1..x..2..x....2..x..0..x....0..x..1..x....0..x..0..x

%e ..x..2..x..1....x..0..x..0....x..0..x..0....x..0..x..2....x..1..x..0

%e ..0..x..0..x....2..x..0..x....0..x..2..x....2..x..0..x....1..x..2..x

%e ..x..2..x..2....x..0..x..2....x..2..x..0....x..0..x..2....x..1..x..0

%Y Column 2 is A062510(n-1)

%Y Column 4 is A230648

%Y Column 6 is A230650

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Oct 27 2013