

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*(n1)*3^(n2).
G.f.: 4*z^2/(13*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*(n1)*3^(n2), n=1..27);


MATHEMATICA

Table[4*(n1)*3^(n2), {n, 30}] (* Wesley Ivan Hurt, Jan 28 2014 *)


PROG

(MAGMA) [4*(n1)*3^(n2): n in [1..30]]; // Vincenzo Librandi, Jun 09 2011
(PARI) a(n) = 4*(n1)*3^(n2); \\ 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



