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

Author

N. J. A. Sloane, Mar 21 2012

Keywords

• nonn
• more

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)

Crossrefs

Cf. A210109, A209970, A001868.

Formula

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

Extensions

a(1)-a(10) computed by R. J. Mathar, Mar 20 2012

a(13) onwards from N. J. A. Sloane, Mar 21 2012