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%I #49 Jun 10 2023 05:15:11
%S 11,111,112,121,122,1111,1112,1121,1122,1123,1211,1212,1213,1221,1222,
%T 1223,1231,1232,1233,11111,11112,11121,11122,11123,11211,11212,11213,
%U 11221,11222,11223,11231,11232,11233,11234,12111,12112,12113,12121,12122,12123,12131,12132,12133,12134,12211,12212
%N Words over an alphabet of size 9 that are in standard order with at least one letter repeated.
%C We study words made of letters from an alphabet of size b, where b >= 1. (Here b=9.) We assume the letters are labeled {1,2,3,...,b}. There are b^n possible words of length n.
%C We say that a word is in "standard order" if it has the property that whenever a letter i appears, the letter i-1 has already appeared in the word. This implies that all words begin with the letter 1.
%C These are the words described in row b=9 of the array in A278986.
%C This sequence can be potentially expanded by a much more efficient algorithm than the brute-force one presented in the program section.
%D Daniel Devatman Hromada, Integer-based nomenclature for the ecosystem of repetitive expressions in complete works of William Shakespeare, submitted to special issue of Argument and Computation on Rhetorical Figures in Computational Argument Studies, 2016.
%H Daniel Devatman Hromada, <a href="/A273977/b273977.txt">List of n, a(n) for n = 1..142407</a> (All words with at most 10 digits.)
%H Daniel Devatman Hromada, <a href="https://doi.org/10.25624/kuenste-1331">Integer-based nomenclature for the ecosystem of repetitive expressions in complete works of William Shakespeare</a>, August 2018.
%H Joerg Arndt and N. J. A. Sloane, <a href="/A278984/a278984.txt">Counting Words that are in "Standard Order"</a>
%t Select[Range[2*10^4], And[Max[DigitCount@ #] >= 2, Range@ Length@ Union@ # == DeleteDuplicates@ # &@ IntegerDigits@ #] &] (* _Michael De Vlieger_, Nov 10 2016 *)
%Y Cf. A278987.
%K base,easy,nonn
%O 1,1
%A _Daniel Devatman Hromada_, Nov 10 2016
%E Edited by _N. J. A. Sloane_, Dec 06 2016
%E Duplicated terms removed from b-file by _Andrew Howroyd_, Feb 27 2018
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