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A342483
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a(n) = binomial(n,2)*(2^(n-2) - n).
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0
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0, 30, 150, 525, 1568, 4284, 11070, 27555, 66792, 158730, 371462, 858585, 1964160, 4454136, 10024254, 22410063, 49803560, 110096070, 242215974, 530573637, 1157621280, 2516574900, 5452586750, 11777596155, 25367140008, 54492385794, 116769410310, 249644959665
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OFFSET
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4,2
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COMMENTS
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a(n) is the number of ternary strings of length n with at least one 0, at least two 1's, and two 2's.
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LINKS
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FORMULA
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G.f.: x^5*(30 - 150*x + 285*x^2 - 262*x^3 + 124*x^4 - 24*x^5)/((1 - x)^4*(1 - 2*x)^3). - Stefano Spezia, Mar 14 2021
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EXAMPLE
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a(7)=525 since the strings are the 210 permutations of 2211000, the 210 permutations of 2211100 and the 105 permutations of 2211110.
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MATHEMATICA
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LinearRecurrence[{10, -42, 96, -129, 102, -44, 8}, {0, 30, 150, 525, 1568, 4284, 11070}, 30] (* Harvey P. Dale, May 17 2024 *)
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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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