editing

approved

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

allocated for R. H. Hardin

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

3, 11, 11, 37, 76, 37, 129, 521, 521, 129, 450, 3588, 6958, 3588, 450, 1568, 24719, 94102, 94102, 24719, 1568, 5464, 170270, 1272579, 2504637, 1272579, 170270, 5464, 19041, 1172854, 17207275, 66684606, 66684606, 17207275, 1172854, 19041, 66354

1,1

Table starts

......3........11...........37.............129.................450

.....11........76..........521............3588...............24719

.....37.......521.........6958...........94102.............1272579

....129......3588........94102.........2504637............66684606

....450.....24719......1272579........66684606..........3495632937

...1568....170270.....17207275......1775039591........183196162778

...5464...1172854....232668433.....47248648693.......9600712297741

..19041...8078859...3146033503...1257683786423.....503143350126954

..66354..55648831..42539187117..33477537844376...26368170190670693

.231230.383320506.575194892084.891118676917809.1381873328000465699

Empirical for column k:

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

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

k=3: [order 20]

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

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

Some solutions for n=3 k=4

..0..1..1..1..1....0..1..1..0..1....0..1..1..1..1....0..1..1..1..0

..0..1..0..1..1....0..0..0..1..1....0..1..0..1..1....0..0..1..0..0

..1..0..1..1..1....0..0..1..0..1....1..1..0..0..0....0..1..0..1..1

..1..0..0..0..0....0..1..0..1..1....1..1..0..0..0....1..0..0..0..1

allocated

nonn,tabl

R. H. Hardin, Nov 17 2013

approved

editing

allocated for R. H. Hardin

allocated

approved