Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #4 Jan 01 2015 10:14:34
%S 81,540,540,3640,800,3640,24208,1400,1400,24208,162016,3072,2000,3072,
%T 162016,1081504,8536,2600,2600,8536,1081504,7227096,15888,5000,3744,
%U 5000,15888,7227096,48272160,44464,7784,7496,7496,7784,44464,48272160
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock diagonal maximum minus antidiagonal minimum unequal to its neighbors horizontally, vertically, diagonally and antidiagonally
%C Table starts
%C .........81....540...3640..24208.162016.1081504.7227096.48272160.322493040
%C ........540....800...1400...3072...8536...15888...44464....94416....273808
%C .......3640...1400...2000...2600...5000....7784...17000....28520.....65000
%C ......24208...3072...2600...3744...7496....8272...15680....31824.....94016
%C .....162016...8536...5000...7496...8000...12680...20000....33416.....68000
%C ....1081504..15888...7784...8272..12680...12800...20864....36352.....99200
%C ....7227096..44464..17000..15680..20000...20864...32000....41600.....80000
%C ...48272160..94416..28520..31824..33416...36352...41600....59904....119936
%C ..322493040.273808..65000..94016..68000...99200...80000...119936....128000
%C .2154281664.562320.111464.104272.116360..108800..124544...132352....202880
%H R. H. Hardin, <a href="/A253468/b253468.txt">Table of n, a(n) for n = 1..3360</a>
%F Empirical for diagonal and column k:
%F diagonal: a(n) = 16*a(n-4) for n>5
%F k=1: a(n) = 2*a(n-1) +27*a(n-2) +30*a(n-3) -7*a(n-4) -8*a(n-5) -75*a(n-6) -48*a(n-7) -16*a(n-8)
%F k=2: a(n) = 5*a(n-2) +8*a(n-4) -12*a(n-6) for n>7
%F k=3: a(n) = 5*a(n-2) -4*a(n-4) for n>6
%F k=4: a(n) = a(n-2) +16*a(n-4) -16*a(n-6) for n>8
%F k=5: a(n) = 5*a(n-2) -4*a(n-4) for n>6
%F k=6: a(n) = a(n-2) +16*a(n-4) -16*a(n-6) for n>8
%F k=7: a(n) = 5*a(n-2) -4*a(n-4) for n>6
%e Some solutions for n=4 k=4
%e ..0..1..0..1..1....1..0..1..0..1....0..2..0..2..1....1..2..1..2..2
%e ..2..0..1..0..1....1..2..1..2..1....2..1..1..0..2....2..1..2..1..2
%e ..0..2..1..2..1....2..1..2..1..2....1..2..0..1..1....0..1..0..1..0
%e ..2..1..2..1..1....0..1..0..1..0....2..1..1..0..2....2..0..1..0..1
%e ..0..1..0..1..1....1..0..1..0..1....1..1..0..0..0....2..1..1..2..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 01 2015