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A278988 a(n) is the number of words of length n over an alphabet of size 3 that are in standard order and which have the property that every letter that appears in the word is repeated.

%I A278988 #15 Nov 26 2017 09:44:14
%S A278988 0,0,1,1,4,11,41,162,610,2165,7327,23948,76352,239175,739909,2268710,
%T A278988 6912430,20966441,63390587,191220048,575888044,1732382363,5207108161,
%U A278988 15642295562,46970926394,141005053341,423208097431,1270026944852,3810919694680,11434503913775,34307135619197
%N A278988 a(n) is the number of words of length n over an alphabet of size 3 that are in standard order and which have the property that every letter that appears in the word is repeated.
%H A278988 Joerg Arndt and N. J. A. Sloane, <a href="/A278984/a278984.txt">Counting Words that are in "Standard Order"</a>
%F A278988 Conjectures from _Colin Barker_, Nov 25 2017: (Start)
%F A278988 G.f.: x^2*(1 - 9*x + 34*x^2 - 71*x^3 + 100*x^4 - 97*x^5 + 52*x^6 - 12*x^7) / ((1 - x)^3*(1 - 2*x)^2*(1 - 3*x)).
%F A278988 a(n) = (2*(3+3^n) - 3*(2+2^n)*n + 6*n^2) / 12 for n>3.
%F A278988 a(n) = 10*a(n-1) - 40*a(n-2) + 82*a(n-3) - 91*a(n-4) + 52*a(n-5) - 12*a(n-6) for n>9.
%F A278988 (End)
%Y A278988 A row of the array in A278987.
%K A278988 nonn
%O A278988 0,5
%A A278988 _N. J. A. Sloane_, Dec 06 2016