A231957 - OEIS

%I #4 Nov 15 2013 19:34:41

%S 4,18,18,64,142,64,236,1034,1034,236,888,7756,14842,7756,888,3336,

%T 58350,220472,220472,58350,3336,12512,438540,3292876,6517534,3292876,

%U 438540,12512,46928,3295580,49124582,193955142,193955142,49124582,3295580,46928

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

%C Table starts

%C ......4.........18............64..............236.................888

%C .....18........142..........1034.............7756...............58350

%C .....64.......1034.........14842...........220472.............3292876

%C ....236.......7756........220472..........6517534...........193955142

%C ....888......58350.......3292876........193955142.........11501370840

%C ...3336.....438540......49124582.......5764579644........681107245458

%C ..12512....3295580.....732691918.....171279257338......40322931224352

%C ..46928...24766738...10928482748....5089308419738....2387295795105696

%C .176032..186126146..163005613290..151223178459482..141340282653200376

%C .660320.1398767358.2431334781688.4493424899719612.8368067905547685676

%H R. H. Hardin, <a href="/A231957/b231957.txt">Table of n, a(n) for n = 1..287</a>

%F Empirical for column k:

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

%F k=2: a(n) = 7*a(n-1) +2*a(n-2) +13*a(n-3) +8*a(n-4)

%F k=3: [order 12]

%F k=4: [order 26]

%F k=5: [order 50]

%e Some solutions for n=3 k=4

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 15 2013