A233989 - OEIS

%I #4 Dec 18 2013 08:06:39

%S 56,236,236,976,1540,976,4064,9632,9632,4064,16880,62040,92320,62040,

%T 16880,70176,393396,914000,914000,393396,70176,291648,2520604,8950496,

%U 14319916,8950496,2520604,291648,1212224,16042420,88388464,218943540

%N T(n,k)=Number of (n+1)X(k+1) 0..4 arrays with every 2X2 subblock having the sum of the squares of the edge differences equal to 10 (10 maximizes T(1,1)), and no two adjacent values equal

%C Table starts

%C ......56.......236........976.........4064..........16880............70176

%C .....236......1540.......9632........62040.........393396..........2520604

%C .....976......9632......92320.......914000........8950496.........88388464

%C ....4064.....62040.....914000.....14319916......218943540.......3423714364

%C ...16880....393396....8950496....218943540.....5240298896.....128552152496

%C ...70176...2520604...88388464...3423714364...128552152496....5022726159372

%C ..291648..16042420..869143232..52813238148..3112596618224..191944315497416

%C .1212224.102569896.8570819600.823369058112.76199608327632.7487035849093952

%H R. H. Hardin, <a href="/A233989/b233989.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

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

%F k=2: [order 13]

%F k=3: [order 25]

%F k=4: [order 78]

%e Some solutions for n=3 k=4

%e ..0..1..0..1..0....0..1..3..4..2....0..2..3..1..3....0..1..0..2..4

%e ..1..3..1..3..1....2..0..1..3..1....1..0..2..0..2....1..3..2..3..2

%e ..2..4..3..2..0....3..1..3..2..3....3..2..3..2..3....2..1..3..1..3

%e ..1..3..1..0..1....2..0..1..0..1....1..0..1..0..2....4..3..4..3..4

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 18 2013