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A237574 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with the upper median minus the lower median of every 2X2 subblock differing from its horizontal and vertical neighbors by exactly one.

%I A237574 #6 Jul 23 2025 10:19:20
%S A237574 256,1876,1876,13924,24332,13924,103264,315664,315664,103264,769680,
%T A237574 4146324,7379204,4146324,769680,5705156,54395184,173478980,173478980,
%U A237574 54395184,5705156,42501300,712810024,4093774632,7415425124,4093774632
%N A237574 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with the upper median minus the lower median of every 2X2 subblock differing from its horizontal and vertical neighbors by exactly one.
%C A237574 Table starts
%C A237574 .......256.........1876..........13924............103264...............769680
%C A237574 ......1876........24332.........315664...........4146324.............54395184
%C A237574 .....13924.......315664........7379204.........173478980...........4093774632
%C A237574 ....103264......4146324......173478980........7415425124.........313460630304
%C A237574 ....769680.....54395184.....4093774632......313460630304.......23898935623162
%C A237574 ...5705156....712810024....95639726868....13253873415032.....1807232491974520
%C A237574 ..42501300...9341685548..2255748816966...561018557350096...138024943528283880
%C A237574 .315065200.122455823868.52746091216472.23744013911896432.10448941120238123892
%H A237574 R. H. Hardin, <a href="/A237574/b237574.txt">Table of n, a(n) for n = 1..84</a>
%F A237574 Empirical for column k:
%F A237574 k=1: [linear recurrence of order 14] for n>15
%F A237574 k=2: [order 45]
%e A237574 Some solutions for n=2 k=4
%e A237574 ..0..0..0..1..1....0..0..1..1..3....0..0..1..0..0....0..0..1..2..0
%e A237574 ..0..2..1..2..3....1..0..3..0..0....1..2..1..0..3....0..0..1..1..2
%e A237574 ..3..3..2..0..2....0..1..1..2..0....2..3..3..1..0....3..1..2..3..2
%K A237574 nonn,tabl
%O A237574 1,1
%A A237574 _R. H. Hardin_, Feb 09 2014