cp's OEIS Frontend

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.

%I A273978 #18 Dec 06 2016 20:39:43
%S A273978 11,111,1111,1122,1212,1221,11111,11122,11212,11221,11222,12112,12121,
%T A273978 12122,12211,12212,12221,111111,111122,111212,111221,111222,112112
%N 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.
%C A273978 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 A273978 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 A273978 These are the words described in row b=9 of the array in A278987.
%D A273978 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.
%H A273978 Daniel Devatman Hromada, <a href="/A273978/b273978.txt">Table of n, a(n) for n = 1..4360</a>
%H A273978 Joerg Arndt and N. J. A. Sloane, <a href="/A278984/a278984.txt">Counting Words that are in "Standard Order"</a>
%o A273978 #PERL checking whether numbers listed in A273977 and given in standard input belong to the current sequence
%o A273978 OUTER: while (<>) {
%o A273978 my %d;
%o A273978 $i=$_;
%o A273978 chop $i;
%o A273978 for $d (split //,$i) {
%o A273978 (exists $d{$d}) ? ($d{$d}++) : ($d{$d}=1);
%o A273978 }
%o A273978 for $k (keys %d) {
%o A273978 next OUTER if ($d{$k}<2);
%o A273978 }
%o A273978 print "$i\n";
%o A273978 }
%Y A273978 Subset of A273977.
%Y A273978 Cf. A278987.
%K A273978 base,easy,nonn
%O A273978 1,1
%A A273978 _Daniel Devatman Hromada_, Nov 10 2016
%E A273978 Edited by _N. J. A. Sloane_, Dec 06 2016