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A240338
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T(n,k)=Number of nXk 0..3 arrays with no element equal to two plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4
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6
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2, 4, 4, 7, 15, 7, 11, 48, 48, 11, 16, 125, 316, 125, 16, 22, 284, 1543, 1543, 284, 22, 29, 582, 6271, 14456, 6271, 582, 29, 37, 1097, 22116, 110327, 110327, 22116, 1097, 37, 46, 1932, 69596, 716770, 1607848, 716770, 69596, 1932, 46, 56, 3219, 199504, 4106515
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OFFSET
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1,1
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COMMENTS
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Table starts
..2....4.......7........11...........16............22.............29
..4...15......48.......125..........284...........582...........1097
..7...48.....316......1543.........6271.........22116..........69596
.11..125....1543.....14456.......110327........716770........4106515
.16..284....6271....110327......1607848......19629542......208224462
.22..582...22116....716770.....19629542.....455506837.....9073358239
.29.1097...69596...4106515....208224462....9073358239...342013040533
.37.1932..199504..21225132...1979743527..160455447637.11361329151015
.46.3219..528924.100450928..17168302936.2579449716281
.56.5123.1310622.439636230.137234695613
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..111
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FORMULA
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Empirical for column k:
k=1: a(n) = (1/2)*n^2 + (1/2)*n + 1
k=2: [polynomial of degree 5] for n>2
k=3: [polynomial of degree 13] for n>12
k=4: [polynomial of degree 30] for n>35
k=5: [polynomial of degree 69] for n>88
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..3..3....0..0..0..0....0..0..0..0....3..0..0..3....0..3..3..3
..0..0..3..3....0..3..0..3....0..0..3..3....0..3..3..2....0..0..3..2
..3..3..2..1....0..0..3..2....0..3..2..2....3..0..2..2....3..3..3..0
..3..2..1..2....0..0..0..0....0..3..2..0....3..3..2..0....3..2..2..2
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CROSSREFS
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Column 1 is A000124
Sequence in context: A268995 A205744 A237859 * A227103 A223644 A223637
Adjacent sequences: A240335 A240336 A240337 * A240339 A240340 A240341
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Apr 04 2014
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STATUS
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approved
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