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%I #4 Jan 17 2015 09:45:59
%S 512,3328,3328,20480,31632,20480,119040,288000,296960,119040,679936,
%T 2546432,3939840,2589968,679936,3825920,22201600,52394496,50414592,
%U 22729728,3825920,21426176,192159408,677982208,1052857184,659280384
%N T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock diagonal maximum minus antidiagonal minimum nondecreasing horizontally, vertically and ne-to-sw antidiagonally
%C Table starts
%C .......512.........3328..........20480...........119040.............679936
%C ......3328........31632.........288000..........2546432...........22201600
%C .....20480.......296960........3939840.........52394496..........677982208
%C ....119040......2589968.......50414592.......1052857184........20975776000
%C ....679936.....22729728......659280384......21171373312.......633276761856
%C ...3825920....195774608.....8536982016.....423305690976.....19275379654400
%C ..21426176...1689797632...111370158592....8407169495552....580087707480832
%C .119525632..14500025360..1445588517376..166630395772512..17553685478957824
%C .665944064.124544611328.18809857917440.3301057791676672.528547039227200256
%H R. H. Hardin, <a href="/A253871/b253871.txt">Table of n, a(n) for n = 1..288</a>
%F Empirical for column k:
%F k=1: a(n) = 8*a(n-1) -7*a(n-2) -56*a(n-3) +120*a(n-4) -64*a(n-5)
%F k=2: [order 17]
%F k=3: [order 17] for n>18
%F k=4: [order 80] for n>85
%F Empirical for row n:
%F n=1: a(n) = 8*a(n-1) -7*a(n-2) -56*a(n-3) +120*a(n-4) -64*a(n-5)
%F n=2: [order 19]
%F n=3: [order 21]
%F n=4: [order 86] for n>93
%e Some solutions for n=2 k=4
%e ..0..1..1..0..0..0....0..1..1..0..1..1....0..1..0..0..1..0....0..0..1..0..1..1
%e ..0..1..0..0..0..0....0..1..0..0..0..0....1..0..1..0..0..0....1..0..1..1..0..0
%e ..1..1..0..1..1..1....1..0..0..1..1..1....1..0..0..0..1..1....1..1..0..1..1..1
%e ..1..0..0..0..0..1....0..0..1..1..1..0....1..0..1..1..1..1....0..0..0..1..0..1
%Y Column 1 and row 1 are A253537
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 17 2015
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