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A210323 Number of 2-divided words of length n over a 3-letter alphabet. 2

%I

%S 0,3,16,57,192,599,1872,5727,17488,53115,161040,487073,1471680,

%T 4441167,13392272,40355877,121543680,365895947,1101089808,3312442185,

%U 9962240928,29954639751,90049997136,270661616363,813397065024,2444101696683,7343167947040,22059763982001,66263812628160

%N Number of 2-divided words of length n over a 3-letter alphabet.

%C See A210109 for further information.

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

%C 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):

%C 3;

%C 8, 8;

%C 18, 21, 18;

%C 48, 48, 48, 48;

%C 116, 124, 119, 124, 116;

%C 312, 312, 312, 312, 312, 312;

%C 810, 828, 810, 831, 810, 828, 810;

%C 2184, 2184, 2192, 2184, 2184, 2192, 2184, 2184;

%C 5880, 5928, 5880, 5928, 5883, 5928, 5880, 5928, 5880;

%C 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:

%C 3;

%C 16, 1;

%C 57, 16, 0;

%C 192, 78, 6, 0;

%C 599, 324, 56, 0, 0;

%C 1872, 1141, 343, 15, 0, 0;

%C 5727, 3885, 1534, 166, 0, 0, 0;

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

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

%C 161040, 126604, ...

%C - _R. J. Mathar_, Mar 25 2012

%C 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

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

%Y Cf. A210109, A209970, A001867.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Mar 20 2012

%E a(1)-a(12) computed by _David Scambler_, Mar 19 2012; a(13) onwards from _N. J. A. Sloane_, Mar 20 2012

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Last modified June 17 18:57 EDT 2019. Contains 324198 sequences. (Running on oeis4.)