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%I #24 May 06 2021 08:11:10
%S 0,0,6,40,186,816,3396,14040,57306,233000,943608,3813000,15378716,
%T 61946640,249260316,1002158880,4026527706,16169288640,64901712996,
%U 260410648680,1044535993800,4188615723280,16792541033556,67309233561240,269746851976156
%N Number of 2-divided words of length n over a 4-letter alphabet.
%C See A210109 for further information.
%C It appears that A027377 gives the number of 2-divided words that have a unique division into two parts. - _David Scambler_, Mar 21 2012
%C From _R. J. Mathar_, Mar 25 2012: (Start)
%C 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:
%C 6;
%C 20, 20;
%C 60, 66, 60;
%C 204, 204, 204, 204;
%C 670, 690, 676, 690, 670;
%C 2340, 2340, 2340, 2340, 2340, 2340;
%C 8160, 8220, 8160, 8226, 8160, 8220, 8160;
%C First column of the following triangle which shows how many words of length n over a 4-letter alphabet are k-divided:
%C 6;
%C 40, 4;
%C 186, 60, 1;
%C 816, 374, 44, 0;
%C 3396, 1960, 450, 12, 0;
%C 14040, 9103, 3175, 275, 0, 0;
%C 57306, 40497, 17977, 2915, 66, 0, 0;
%C 233000, 174127, 91326, 22243, 1318,..
%C (End)
%F a(n) = 4^n - A001868(n) (see A209970 for proof).
%Y Cf. A210109, A209970, A001868.
%K nonn,more
%O 1,3
%A _N. J. A. Sloane_, Mar 21 2012
%E a(1)-a(10) computed by _R. J. Mathar_, Mar 20 2012
%E a(13) onwards from _N. J. A. Sloane_, Mar 21 2012
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