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A287275
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Number of set partitions of [n] such that for each block all absolute differences between consecutive elements are <= three.
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4
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1, 1, 2, 5, 15, 47, 150, 481, 1545, 4965, 15958, 51293, 164871, 529947, 1703418, 5475329, 17599457, 56570281, 181834970, 584475733, 1878691887, 6038716423, 19410365422, 62391120801, 200545011401, 644615789581, 2072001259342, 6660074556205, 21407609138375
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: -(x^3-3*x+1)/((x-1)*(x^3-x^2-3*x+1)).
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EXAMPLE
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a(5) = 47 = 52 - 5 = A000110(5) - 5 counts all set partitions of [5] except: 15|234, 15|23|4, 15|24|3, 15|2|34, 15|2|3|4.
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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