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A210326
Number of 5-divided words of length n over a 3-letter alphabet.
3
0, 0, 0, 0, 0, 0, 15, 166, 1135, 5865, 26170, 105224, 396082, 1419981, 4916112
OFFSET
1,7
COMMENTS
See A210109 for further information.
Row sums of the following table which shows how many words of length n over a 3-letter alphabet are 5-divided in k>=1 different ways:
15;
103,43,20;
546,236,162,84,28,51,16,8,5;
2118,1211,848,480,...
- R. J. Mathar, Mar 25 2012
REFERENCES
Computed by David Scambler, Mar 19 2012
PROG
(Python)
from itertools import product, combinations, permutations
def is5div(b):
for i, j, k, l in combinations(range(1, len(b)), 4):
divisions = [b[:i], b[i:j], b[j:k], b[k:l], b[l:]]
all_greater = True
for p, bp in enumerate(permutations(divisions)):
if p == 0: continue
if b >= "".join(bp): all_greater = False; break
if all_greater: return True
return False
def a(n): return sum(is5div("".join(b)) for b in product("012", repeat=n))
print([a(n) for n in range(1, 10)]) # Michael S. Branicky, Aug 28 2021
CROSSREFS
KEYWORD
nonn,more
AUTHOR
N. J. A. Sloane, Mar 20 2012
EXTENSIONS
a(14)-a(15) from Michael S. Branicky, Aug 28 2021
STATUS
approved