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A295200
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Number of nX3 0..1 arrays with each 1 horizontally or vertically adjacent to 2 or 4 1s.
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1
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1, 3, 8, 14, 25, 53, 111, 217, 426, 860, 1733, 3453, 6885, 13791, 27616, 55198, 110341, 220737, 441563, 883037, 1765930, 3532004, 7064241, 14128249, 28256121, 56512619, 113025848, 226051086, 452101185, 904203357, 1808408311, 3616815025
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = 2*a(n-1) -a(n-2) +2*a(n-3) +a(n-4) -2*a(n-5).
Empirical formula is true (see link).
G.f.: (x+x^2+3*x^3-x^4-2*x^5)/(1-2*x+x^2-2*x^3-x^4+2*x^5). (End)
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EXAMPLE
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Some solutions for n=7
..1..1..0. .0..0..0. .0..0..0. .0..1..1. .0..0..0. .1..1..1. .0..0..0
..1..1..0. .0..1..1. .1..1..0. .0..1..1. .1..1..0. .1..0..1. .0..0..0
..0..0..0. .1..1..1. .1..1..0. .0..0..0. .1..1..0. .1..0..1. .0..0..0
..0..1..1. .1..1..0. .0..0..0. .0..0..0. .0..0..0. .1..0..1. .0..0..0
..0..1..1. .0..0..0. .1..1..0. .0..0..0. .1..1..0. .1..0..1. .1..1..0
..0..0..0. .0..1..1. .1..1..0. .0..0..0. .1..1..1. .1..1..1. .1..1..1
..0..0..0. .0..1..1. .0..0..0. .0..0..0. .0..1..1. .0..0..0. .0..1..1
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MAPLE
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f:= gfun:-rectoproc({a(n) = 2*a(n-1) -a(n-2) +2*a(n-3) +a(n-4) -2*a(n-5), a(1)=1, a(2)=3, a(3)=8, a(4)=14, a(5)=25}, a(n), remember):
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MATHEMATICA
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LinearRecurrence[{2, -1, 2, 1, -2}, {1, 3, 8, 14, 25}, 32] (* Jean-François Alcover, Aug 27 2022 *)
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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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