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Number of (n+1) X (1+1) 0..3 arrays with the maximum plus the upper median plus the minimum of every 2X2 2 X 2 subblock differing from its horizontal and vertical neighbors by exactly one.

Column 1 of A237677.

Empirical: a(n) = 1464*a(n-4) +21444*a(n-6) -217012*a(n-8) -5585804*a(n-10) -12617424*a(n-12) +351921344*a(n-14) +2542892384*a(n-16) +1019240768*a(n-18) -42797024832*a(n-20) -123435815936*a(n-22) +85546957824*a(n-24) +742456289792*a(n-26) +481891066880*a(n-28) -1227137187840*a(n-30) -1305858437120*a(n-32) +134355173376*a(n-34) +344315133952*a(n-36) -1108344832*a(n-38) -26916945920*a(n-40) -3468689408*a(n-42) -369098752*a(n-44) for n>45.

Cf. A237677.

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R. H. Hardin, <a href="/A237672/b237672.txt">Table of n, a(n) for n = 1..210</a>

allocated for R. H. Hardin

Number of (n+1)X(1+1) 0..3 arrays with the maximum plus the upper median plus the minimum of every 2X2 subblock differing from its horizontal and vertical neighbors by exactly one

256, 1564, 9647, 63000, 412120, 2668500, 17280632, 112196812, 729345568, 4730716616, 30705881416, 199250972104, 1294118583944, 8396039853104, 54516655728608, 353723940339776, 2297049424994128, 14903574260972720

1,1

Column 1 of A237677

Empirical: a(n) = 1464*a(n-4) +21444*a(n-6) -217012*a(n-8) -5585804*a(n-10) -12617424*a(n-12) +351921344*a(n-14) +2542892384*a(n-16) +1019240768*a(n-18) -42797024832*a(n-20) -123435815936*a(n-22) +85546957824*a(n-24) +742456289792*a(n-26) +481891066880*a(n-28) -1227137187840*a(n-30) -1305858437120*a(n-32) +134355173376*a(n-34) +344315133952*a(n-36) -1108344832*a(n-38) -26916945920*a(n-40) -3468689408*a(n-42) -369098752*a(n-44) for n>45

Some solutions for n=4

..2..2....0..0....2..2....2..0....3..2....0..2....2..3....2..2....0..2....3..1

..0..1....0..1....0..1....1..0....3..1....0..3....0..3....0..2....3..0....3..3

..2..0....1..0....0..2....0..3....2..2....1..3....2..1....0..3....1..3....2..0

..0..2....0..2....0..0....0..0....2..3....0..2....2..0....1..0....3..1....3..2

..3..1....2..0....2..1....3..1....3..3....1..2....3..0....0..2....3..0....3..0

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nonn

R. H. Hardin, Feb 11 2014

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