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A255623
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Number of length n+1 0..2 arrays with at most two downsteps in every n consecutive neighbor pairs.
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1
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9, 27, 81, 237, 651, 1647, 3834, 8272, 16698, 31824, 57720, 100296, 167898, 272034, 428247, 657153, 985663, 1448409, 2089395, 2963895, 4140621, 5704185, 7757880, 10426806, 13861368, 18241174, 23779362, 30727386, 39380292, 50082516, 63234237
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = (1/40320)*n^8 + (11/10080)*n^7 + (7/576)*n^6 + (7/180)*n^5 + (847/5760)*n^4 + (1007/1440)*n^3 + (1237/672)*n^2 + (913/280)*n + 3.
Empirical g.f.: x*(9 - 54*x + 162*x^2 - 276*x^3 + 300*x^4 - 216*x^5 + 99*x^6 - 26*x^7 + 3*x^8) / (1 - x)^9. - Colin Barker, Jan 21 2018
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EXAMPLE
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Some solutions for n=4:
..0....1....2....1....2....2....2....0....2....1....2....0....1....2....1....0
..0....0....0....1....0....0....0....1....0....2....2....0....1....1....2....0
..1....1....0....2....2....0....1....0....0....0....0....2....1....0....0....0
..2....1....1....0....0....1....0....0....1....2....2....2....1....0....1....2
..1....0....2....1....2....1....1....0....0....1....0....1....0....1....0....2
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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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