A210424 Number of 2-divided words of length n over a 4-letter alphabet.

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

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

From R. J. Mathar, Mar 25 2012: (Start)

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,..

(End)

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: A005553 A335232 A055344 * A367778 A292029 A227124

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