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A120908
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Sum of the lengths of the drops in all ternary words of length n on {0,1,2}. The drops of a ternary word on {0,1,2} are the subwords 10,20 and 21, their lengths being the differences 1, 2 and 1, respectively.
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10
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0, 4, 24, 108, 432, 1620, 5832, 20412, 69984, 236196, 787320, 2598156, 8503056, 27634932, 89282088, 286978140, 918330048, 2927177028, 9298091736, 29443957164, 92980917360, 292889889684, 920511081864, 2887057484028
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OFFSET
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1,2
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COMMENTS
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a(n) = 4*A027471(n).
a(n) = Sum_{k>=0} k*A120907(n,k).
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..400
Franck Ramaharo, Statistics on some classes of knot shadows, arXiv:1802.07701 [math.CO], 2018.
Index entries for linear recurrences with constant coefficients, signature (6,-9).
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FORMULA
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a(n) = 4*(n-1)*3^(n-2).
G.f.: 4*z^2/(1-3*z)^2.
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EXAMPLE
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a(2)=4 because the ternary words 00,01,02,11,12 and 22 have no drops, each of the words 10 and 21 has one drop of length 1 and the word 20 has one drop of length 2.
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MAPLE
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seq(4*(n-1)*3^(n-2), n=1..27);
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MATHEMATICA
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Table[4*(n-1)*3^(n-2), {n, 30}] (* Wesley Ivan Hurt, Jan 28 2014 *)
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PROG
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(Magma) [4*(n-1)*3^(n-2): n in [1..30]]; // Vincenzo Librandi, Jun 09 2011
(PARI) a(n) = 4*(n-1)*3^(n-2); \\ Altug Alkan, May 16 2018
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CROSSREFS
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Cf. A027471, A120906, A120907.
Sequence in context: A006736 A165752 A166036 * A145655 A265975 A306610
Adjacent sequences: A120905 A120906 A120907 * A120909 A120910 A120911
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KEYWORD
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nonn,easy
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AUTHOR
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Emeric Deutsch, Jul 15 2006
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STATUS
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approved
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