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A341703
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a(n) = 6*binomial(n,4) + 2*binomial(n,2) + 1.
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2
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1, 1, 3, 7, 19, 51, 121, 253, 477, 829, 1351, 2091, 3103, 4447, 6189, 8401, 11161, 14553, 18667, 23599, 29451, 36331, 44353, 53637, 64309, 76501, 90351, 106003, 123607, 143319, 165301, 189721, 216753, 246577, 279379, 315351, 354691, 397603, 444297, 494989, 549901
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OFFSET
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0,3
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COMMENTS
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a(n) is the number of ternary strings of length n that contain either none or two 0's and either none or two 1's.
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LINKS
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FORMULA
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E.g.f.: exp(x)*(1 + x^2/2)^2.
O.g.f.:(1 - 4*x + 8*x^2 - 8*x^3 + 9*x^4)/(1 - x)^5.
a(n) = (4 - 10*n + 15*n^2 - 6*n^3 + n^4)/4. (End)
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EXAMPLE
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a(6)=121 since the strings are the 90 permutations of 110022, the 15 permutations of 002222, the 15 permutations of 112222, and 222222.
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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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