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A255661
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Number of length n+1 0..3 arrays with at most two downsteps in every n consecutive neighbor pairs.
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1
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16, 64, 255, 968, 3340, 10320, 28722, 72920, 171106, 375388, 777452, 1532064, 2891360, 5253680, 9231663, 15745452, 26148180, 42392440, 67248205, 104584680, 159730860, 239932160, 354923400, 517641696, 745106454, 1059497716, 1489468594
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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) = (1/39916800)*n^11 + (1/518400)*n^10 + (1/15120)*n^9 + (137/120960)*n^8 + (12461/1209600)*n^7 + (8251/172800)*n^6 + (56011/362880)*n^5 + (14791/25920)*n^4 + (278149/151200)*n^3 + (8149/2100)*n^2 + (2539/462)*n + 4.
Empirical g.f.: x*(16 - 128*x + 543*x^2 - 1388*x^3 + 2394*x^4 - 2964*x^5 + 2683*x^6 - 1760*x^7 + 814*x^8 - 252*x^9 + 47*x^10 - 4*x^11) / (1 - x)^12. - Colin Barker, Jan 21 2018
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EXAMPLE
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Some solutions for n=4:
..0....2....1....2....1....1....1....3....2....3....0....0....0....3....1....1
..2....3....1....2....2....3....1....0....0....0....1....3....2....3....2....3
..1....0....2....2....0....0....3....0....3....0....1....0....0....0....1....0
..3....3....3....0....3....0....0....0....1....1....3....3....0....3....1....2
..3....0....2....3....0....0....0....3....1....0....3....1....2....3....2....0
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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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