A232038 - OEIS

%I #4 Nov 17 2013 07:18:04

%S 3,11,11,37,76,37,129,521,521,129,450,3588,6958,3588,450,1568,24719,

%T 94102,94102,24719,1568,5464,170270,1272579,2504637,1272579,170270,

%U 5464,19041,1172854,17207275,66684606,66684606,17207275,1172854,19041,66354

%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every element equal to some horizontal, vertical or antidiagonal neighbor, with top left element zero

%C Table starts

%C ......3........11...........37.............129.................450

%C .....11........76..........521............3588...............24719

%C .....37.......521.........6958...........94102.............1272579

%C ....129......3588........94102.........2504637............66684606

%C ....450.....24719......1272579........66684606..........3495632937

%C ...1568....170270.....17207275......1775039591........183196162778

%C ...5464...1172854....232668433.....47248648693.......9600712297741

%C ..19041...8078859...3146033503...1257683786423.....503143350126954

%C ..66354..55648831..42539187117..33477537844376...26368170190670693

%C .231230.383320506.575194892084.891118676917809.1381873328000465699

%H R. H. Hardin, <a href="/A232038/b232038.txt">Table of n, a(n) for n = 1..312</a>

%F Empirical for column k:

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

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

%F k=3: [order 20]

%F k=4: [order 42] for n>44

%F k=5: [order 95] for n>97

%e Some solutions for n=3 k=4

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 17 2013