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%I #4 Feb 15 2014 18:03:59
%S 256,1632,1632,10316,15260,10316,66512,142488,142488,66512,431640,
%T 1365710,1926461,1365710,431640,2776536,13009850,26467386,26467386,
%U 13009850,2776536,17920936,123407764,362996768,533139326,362996768
%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with the maximum plus the lower median of every 2X2 subblock differing from its horizontal and vertical neighbors by exactly one
%C Table starts
%C ........256..........1632...........10316............66512...........431640
%C .......1632.........15260..........142488..........1365710.........13009850
%C ......10316........142488.........1926461.........26467386........362996768
%C ......66512.......1365710........26467386........533139326......10733520644
%C .....431640......13009850.......362996768......10733520644.....318431976402
%C ....2776536.....123407764......4957001920.....216277393666....9401494272628
%C ...17920936....1173616996.....68164733860....4367587791906..279092830922873
%C ..115383848...11179776830....934379485016...88165105669262.8254890731634348
%C ..745952272..106365553324..12832924363235.1776627602822848
%C .4801239096.1011373253330.175593729622252
%H R. H. Hardin, <a href="/A237927/b237927.txt">Table of n, a(n) for n = 1..84</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 30]
%F k=2: [order 93]
%e Some solutions for n=2 k=4
%e ..0..0..3..3..1....0..0..0..3..1....0..2..1..1..3....0..2..2..0..3
%e ..2..3..1..2..1....3..2..2..0..2....2..0..1..0..0....0..1..0..1..0
%e ..1..0..0..3..2....1..1..1..3..3....0..3..1..2..2....1..0..2..1..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 15 2014