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A273977 Words over an alphabet of size 9 that are in standard order with at least one letter repeated. 3
11, 111, 112, 121, 122, 1111, 1112, 1121, 1122, 1123, 1211, 1212, 1213, 1221, 1222, 1223, 1231, 1232, 1233, 11111, 11112, 11121, 11122, 11123, 11211, 11212, 11213, 11221, 11222, 11223, 11231, 11232, 11233, 11234, 12111, 12112, 12113, 12121, 12122, 12123, 12131, 12132, 12133, 12134, 12211, 12212 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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.
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.
These are the words described in row b=9 of the array in A278986.
This sequence can be potentially expanded by a much more efficient algorithm than the brute-force one presented in the program section.
REFERENCES
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.
LINKS
Daniel Devatman Hromada, List of n, a(n) for n = 1..142407 (All words with at most 10 digits.)
Joerg Arndt and N. J. A. Sloane, Counting Words that are in "Standard Order"
MATHEMATICA
Select[Range[2*10^4], And[Max[DigitCount@ #] >= 2, Range@ Length@ Union@ # == DeleteDuplicates@ # &@ IntegerDigits@ #] &] (* Michael De Vlieger, Nov 10 2016 *)
CROSSREFS
Cf. A278987.
Sequence in context: A327992 A204847 A098759 * A358441 A135464 A231872
KEYWORD
base,easy,nonn
AUTHOR
EXTENSIONS
Edited by N. J. A. Sloane, Dec 06 2016
Duplicated terms removed from b-file by Andrew Howroyd, Feb 27 2018
STATUS
approved

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Last modified November 29 16:16 EST 2023. Contains 367445 sequences. (Running on oeis4.)