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A120908 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. 10
0, 4, 24, 108, 432, 1620, 5832, 20412, 69984, 236196, 787320, 2598156, 8503056, 27634932, 89282088, 286978140, 918330048, 2927177028, 9298091736, 29443957164, 92980917360, 292889889684, 920511081864, 2887057484028 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) = 4*A027471(n).

a(n) = Sum_{k>=0} k*A120907(n,k).

LINKS

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).

FORMULA

a(n) = 4*(n-1)*3^(n-2).

G.f.: 4*z^2/(1-3*z)^2.

EXAMPLE

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.

MAPLE

seq(4*(n-1)*3^(n-2), n=1..27);

MATHEMATICA

Table[4*(n-1)*3^(n-2), {n, 30}] (* Wesley Ivan Hurt, Jan 28 2014 *)

PROG

(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

CROSSREFS

Cf. A027471, A120906, A120907.

Sequence in context: A006736 A165752 A166036 * A145655 A265975 A306610

Adjacent sequences:  A120905 A120906 A120907 * A120909 A120910 A120911

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, Jul 15 2006

STATUS

approved

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Last modified July 9 22:33 EDT 2020. Contains 335545 sequences. (Running on oeis4.)