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.
Original entry on oeis.org
11, 111, 1111, 1122, 1212, 1221, 11111, 11122, 11212, 11221, 11222, 12112, 12121, 12122, 12211, 12212, 12221, 111111, 111122, 111212, 111221, 111222, 112112
Offset: 1
- 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.
A278986
Array read by antidiagonals downwards: T(b,n) = number of words of length n over an alphabet of size b that are in standard order and which have the property that at least one letter is repeated.
Original entry on oeis.org
0, 1, 0, 1, 1, 0, 1, 4, 1, 0, 1, 8, 4, 1, 0, 1, 16, 14, 4, 1, 0, 1, 32, 41, 14, 4, 1, 0, 1, 64, 122, 51, 14, 4, 1, 0, 1, 128, 365, 187, 51, 14, 4, 1, 0, 1, 256, 1094, 715, 202, 51, 14, 4, 1, 0, 1, 512, 3281, 2795, 855, 202, 51, 14, 4, 1, 0, 1, 1024, 9842, 11051, 3845, 876, 202, 51, 14, 4, 1
Offset: 1
The array begins:
0,.1,..1,...1,...1,...1,...1,....1..; b=1,
0,.1,..4,...8,..16,..32,..64,..128..; b=2,
0,.1,..4,..14,..41,.122,.365,.1094..; b=3,
0,.1,..4,..14,..51,.187,.715,.2795..; b=4,
0,.1,..4,..14,..51,.202,.855,.3845..; b=5,
0,.1,..4,..14,..51,.202,.876,.4111..; b=6,
...
See
A278984 for a closely related array.
The words for b=3 are listed in
A278985, except that the words 1, 12, and 123 must be omitted from that list.
The words for b=9 are listed in
A273977.
-
with(combinat);
f2:=proc(L,b) local t1;i;
t1:=add(stirling2(L,i),i=1..b); if L <= b then t1:=t1-1; fi; t1; end;
Q2:=b->[seq(f2(L,b), L=1..20)];
for b from 1 to 6 do lprint(Q2(b)); od:
Showing 1-2 of 2 results.
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