A232316 - OEIS

%I #6 Nov 22 2013 09:55:51

%S 2,5,5,16,24,13,52,139,115,34,169,853,1202,551,89,549,5241,14042,

%T 10409,2640,233,1784,32089,164014,231454,90157,12649,610,5797,196698,

%U 1905436,5142441,3815483,780922,60605,1597,18837,1205422,22161823,113293694

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

%C Table starts

%C .....2.......5.........16............52..............169.................549

%C .....5......24........139...........853.............5241...............32089

%C ....13.....115.......1202.........14042...........164014.............1905436

%C ....34.....551......10409........231454..........5142441...........113293694

%C ....89....2640......90157.......3815483........161243887..........6736602042

%C ...233...12649.....780922......62897985.......5055954492........400571676322

%C ...610...60605....6764246....1036869496.....158534446141......23818815015639

%C ..1597..290376...58591124...17092731689....4971005036586....1416315842358249

%C ..4181.1391275..507509767..281772661177..155870804492221...84217060496525106

%C .10946.6665999.4395993154.4645005493684.4887484036570530.5007720081104988709

%H R. H. Hardin, <a href="/A232316/b232316.txt">Table of n, a(n) for n = 1..390</a>

%F Empirical for column k:

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

%F k=2: a(n) = 5*a(n-1) -a(n-2)

%F k=3: a(n) = 10*a(n-1) -11*a(n-2) -5*a(n-3) -a(n-4)

%F k=4: a(n) = 19*a(n-1) -44*a(n-2) +43*a(n-3) -19*a(n-4) +4*a(n-5) -2*a(n-6) for n>7

%F k=5: [order 12] for n>13

%F k=6: [order 18] for n>20

%F k=7: [order 37] for n>40

%F Empirical for row n:

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

%F n=2: [order 12] for n>14

%F n=3: [order 32] for n>34

%F n=4: [order 78] for n>82

%e Some.solutions.for.n=3.k=4

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

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

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

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

%Y Column 1 is A001519(n+1)

%Y Column 2 is A004254(n+1)

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 22 2013