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A210424 Number of 2-divided words of length n over a 4-letter alphabet. 2
0, 0, 6, 40, 186, 816, 3396, 14040, 57306, 233000, 943608, 3813000, 15378716, 61946640, 249260316, 1002158880, 4026527706, 16169288640, 64901712996, 260410648680, 1044535993800, 4188615723280, 16792541033556, 67309233561240, 269746851976156 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

See A210109 for further information.

It appears that A027377 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 table which shows how many words of length n over a 4-letter alphabet are 2-divided in k>=1 different ways:

6;

20, 20;

60, 66, 60;

204, 204, 204, 204;

670, 690, 676, 690, 670;

2340, 2340, 2340, 2340, 2340, 2340;

8160, 8220, 8160, 8226, 8160, 8220, 8160;

First column of the following triangle which shows how many words of length n over a 4-letter alphabet are k-divided:

6;

40, 4;

186, 60, 1;

816, 374, 44, 0;

3396, 1960, 450, 12, 0;

14040, 9103, 3175, 275, 0, 0;

57306, 40497, 17977, 2915, 66, 0, 0;

233000, 174127, 91326, 22243, 1318,..

- R. J. Mathar, Mar 25 2012

LINKS

Table of n, a(n) for n=1..25.

FORMULA

a(n) = 4^n - A001868(n) (see A209970 for proof).

CROSSREFS

Cf. A210109, A209970, A001868.

Sequence in context: A001919 A005553 A055344 * A292029 A227124 A232568

Adjacent sequences:  A210421 A210422 A210423 * A210425 A210426 A210427

KEYWORD

nonn,more

AUTHOR

N. J. A. Sloane, Mar 21 2012

EXTENSIONS

a(1)-a(10) computed by R. J. Mathar, Mar 20 2012; a(13) onwards from N. J. A. Sloane, Mar 21 2012

STATUS

approved

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Last modified November 17 23:26 EST 2019. Contains 329242 sequences. (Running on oeis4.)