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A230831
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T(n,k)=Number of nXk 0..3 arrays x(i,j) with each element horizontally, vertically or antidiagonally next to at least one element with value (x(i,j)+1) mod 4 and at least one element with value (x(i,j)-1) mod 4, no adjacent elements equal, and upper left element zero
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8
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0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 6, 8, 6, 0, 0, 16, 10, 10, 16, 0, 0, 44, 38, 62, 38, 44, 0, 0, 124, 130, 176, 176, 130, 124, 0, 0, 354, 456, 734, 898, 734, 456, 354, 0, 0, 1020, 1610, 3034, 4350, 4350, 3034, 1610, 1020, 0, 0, 2956, 5740, 12962, 22852, 29446, 22852, 12962
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OFFSET
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1,5
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COMMENTS
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Table starts
.0...0....0.....0......0.......0........0.........0..........0...........0
.0...2....2.....6.....16......44......124.......354.......1020........2956
.0...2....8....10.....38.....130......456......1610.......5740.......20556
.0...6...10....62....176.....734.....3034.....12962......55806......241462
.0..16...38...176....898....4350....22852....122740.....661598.....3593650
.0..44..130...734...4350...29446...201592...1388526....9649244....67351066
.0.124..456..3034..22852..201592..1807682..16202418..145774974..1316654208
.0.354.1610.12962.122740.1388526.16202418.188719562.2198502114.25739337218
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..199
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 4*a(n-1) -2*a(n-2) -3*a(n-3) -a(n-4) for n>5
k=3: [order 12] for n>17
k=4: [order 46] for n>51
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EXAMPLE
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Some solutions for n=4 k=4
..0..1..2..1....0..1..3..0....0..1..2..1....0..3..0..3....0..1..2..1
..3..0..3..0....3..2..1..2....3..0..3..0....1..2..1..2....3..0..3..0
..2..1..2..1....1..3..0..3....2..1..2..1....0..3..0..3....2..1..2..3
..3..0..3..2....0..2..1..0....3..0..3..0....1..2..1..0....0..3..1..0
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CROSSREFS
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Sequence in context: A181111 A353856 A216800 * A230899 A230805 A230994
Adjacent sequences: A230828 A230829 A230830 * A230832 A230833 A230834
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Oct 30 2013
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STATUS
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approved
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