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A210323 Number of 2-divided words of length n over a 3-letter alphabet. 2
0, 3, 16, 57, 192, 599, 1872, 5727, 17488, 53115, 161040, 487073, 1471680, 4441167, 13392272, 40355877, 121543680, 365895947, 1101089808, 3312442185, 9962240928, 29954639751, 90049997136, 270661616363, 813397065024, 2444101696683, 7343167947040, 22059763982001, 66263812628160 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A210109 for further information.

It appears that A027376 gives the number of 2-divided words that have a unique division into two parts. - David Scambler, Mar 21 2012

Row sums of the following irregular triangle W(n,k) which shows how many words of length n over a 3-letter alphabet are 2-divided in k>=1 different ways (3-letter analog of A209919):

3;

8, 8;

18, 21, 18;

48, 48, 48, 48;

116, 124, 119, 124, 116;

312, 312, 312, 312, 312, 312;

810, 828, 810, 831, 810, 828, 810;

2184, 2184, 2192, 2184, 2184, 2192, 2184, 2184;

5880, 5928, 5880, 5928, 5883, 5928, 5880, 5928, 5880;

First column of the following triangle D(n,k) which shows how many words of length n over a 3-letter alphabet are k-divided:

3;

16, 1;

57, 16, 0;

192, 78, 6, 0;

599, 324, 56, 0, 0;

1872, 1141, 343, 15, 0, 0;

5727, 3885, 1534, 166, 0, 0, 0;

17488, 12630, 6067, 1135, 20, 0, 0, 0;

53115, 40315, 22162, 5865, 351, 0, 0, 0, 0;

161040, 126604, ...

- R. J. Mathar, Mar 25 2012

Speculation: W(2n+1,2)=W(2n+1,1) and W(2n,2) = W(2n,1)+W(n,1). W(3n+1,3)=W(3n+1,1); W(3n+2,3)=W(3n+1,1); W(3n,3) = W(3n,1)+W(n,1). - R. J. Mathar, Mar 27 2012

LINKS

Table of n, a(n) for n=1..29.

FORMULA

a(n) = 3^n - A001867(n) (see A209970 for proof).

CROSSREFS

Cf. A210109, A209970, A001867.

Sequence in context: A027540 A099851 A005550 * A062474 A073999 A259056

Adjacent sequences:  A210320 A210321 A210322 * A210324 A210325 A210326

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mar 20 2012

EXTENSIONS

a(1)-a(12) computed by David Scambler, Mar 19 2012; a(13) onwards from N. J. A. Sloane, Mar 20 2012

STATUS

approved

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Last modified September 24 22:31 EDT 2017. Contains 292441 sequences.