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A273978 List of words of length n over an alphabet of size 9 that are in standard order and which have the property that every letter that appears in the word is repeated. 2
11, 111, 1111, 1122, 1212, 1221, 11111, 11122, 11212, 11221, 11222, 12112, 12121, 12122, 12211, 12212, 12221, 111111, 111122, 111212, 111221, 111222, 112112 (list; graph; refs; listen; history; text; internal format)



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 A278987.


D. D. 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.


Daniel Devatman Hromada, Table of n, a(n) for n = 1..4360

Joerg Arndt and N. J. A. Sloane, Counting Words that are in "Standard Order"


#PERL checking whether numbers listed in A273977 and given in standard input belong to the current sequence

OUTER: while (<>) {

my %d;


chop $i;

for $d (split //, $i) {

(exists $d{$d}) ? ($d{$d}++) : ($d{$d}=1);


for $k (keys %d) {

next OUTER if ($d{$k}<2);


print "$i\n";



Subset of A273977.

Cf. A278987.

Sequence in context: A114397 A336325 A098595 * A334131 A077488 A039988

Adjacent sequences:  A273975 A273976 A273977 * A273979 A273980 A273981




Daniel Devatman Hromada, Nov 10 2016


Edited by N. J. A. Sloane, Dec 06 2016



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Last modified September 17 07:51 EDT 2021. Contains 347478 sequences. (Running on oeis4.)