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A240789
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Number of n X 2 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it or zero plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.
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1
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3, 4, 5, 10, 13, 14, 30, 32, 36, 67, 79, 97, 173, 191, 232, 402, 464, 580, 960, 1104, 1400, 2250, 2637, 3388, 5280, 6255, 8117, 12342, 14819, 19374, 28826, 35008, 46021, 67233, 82554, 108956, 156715, 194316, 257170, 365065, 456688, 605532, 850096, 1071831
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OFFSET
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1,1
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LINKS
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FORMULA
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Empirical: a(n) = 4*a(n-3) + a(n-5) - 3*a(n-6) - 3*a(n-8) - 4*a(n-9) + a(n-11) + 4*a(n-12) + 3*a(n-14) - 2*a(n-17) for n>19.
Empirical g.f.: x*(3 + 4*x + 5*x^2 - 2*x^3 - 3*x^4 - 9*x^5 - 5*x^6 - 13*x^7 - 6*x^8 - 12*x^9 + 7*x^10 + 12*x^11 + 26*x^12 + 8*x^13 - 8*x^14 - 17*x^15 - 5*x^16 + 5*x^17 + 2*x^18) / ((1 - x)*(1 + x)*(1 - x + x^2)*(1 + x + x^2)*(1 - x^2 - x^3)*(1 - 2*x^3)*(1 + x^2 - x^3 + x^4 - x^5)). - Colin Barker, Oct 29 2018
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EXAMPLE
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All solutions for n=4:
..3..3....3..3....3..3....3..3....3..2....3..2....3..3....3..2....3..3....3..3
..2..1....2..2....2..1....2..2....3..1....3..1....2..2....3..1....2..2....2..2
..3..3....3..1....3..3....3..1....2..2....2..1....3..3....2..2....3..1....3..1
..2..2....2..2....2..1....3..2....3..1....3..3....2..2....3..3....3..1....2..1
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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