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A193519
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a(n) = (2/3)*Sum_{i=1..n-1} A000129(i)*3^(n-i).
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2
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0, 0, 2, 10, 40, 144, 490, 1610, 5168, 16320, 50930, 157546, 484120, 1480080, 4507162, 13683050, 41439200, 125259264, 378051170, 1139641930, 3432176008, 10328516880, 31062778570, 93374780426, 280574458640, 842810055360, 2531053642322, 7599494558890, 22813774416760, 68478238362384
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OFFSET
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0,3
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COMMENTS
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Number of ternary words of length n on {0,1,2} containing the subwords 02 or 20. - Philippe Deléham, Apr 27 2012
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LINKS
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FORMULA
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a(n) = 5*a(n-1) - 5*a(n-2) - 3*a(n-3), a(0) = a(1) = 0, a(2) = 2. - Philippe Deléham, Apr 27 2012
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EXAMPLE
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a(3) = 10 because among the 3^3 = 27 ternary words of length 3 only 10, namely 002, 020, 021, 022, 102, 120, 200, 201, 202, 220 contain the subwords 02 or 20. - Philippe Deléham, Apr 27 2012
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MATHEMATICA
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Table[(2*3^n - LucasL[n+1, 2])/2, {n, 0, 30}] (* G. C. Greubel, Jan 05 2022 *)
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PROG
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(Magma) [n le 3 select 2*Floor((n-1)/2) else 5*Self(n-1) -5*Self(n-2) -3*Self(n-3): n in [1..31]]; // G. C. Greubel, Jan 05 2022
(Sage) [(2*3^n - lucas_number2(n+1, 2, -1))/2 for n in (0..30)] # G. C. Greubel, Jan 05 2022
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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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