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%I #21 Aug 28 2021 12:45:53
%S 0,0,0,0,0,0,15,166,1135,5865,26170,105224,396082,1419981,4916112
%N Number of 5-divided words of length n over a 3-letter alphabet.
%C See A210109 for further information.
%C 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:
%C 15;
%C 103,43,20;
%C 546,236,162,84,28,51,16,8,5;
%C 2118,1211,848,480,...
%C - _R. J. Mathar_, Mar 25 2012
%D Computed by David Scambler, Mar 19 2012
%o (Python)
%o from itertools import product, combinations, permutations
%o def is5div(b):
%o for i, j, k, l in combinations(range(1, len(b)), 4):
%o divisions = [b[:i], b[i:j], b[j:k], b[k:l], b[l:]]
%o all_greater = True
%o for p, bp in enumerate(permutations(divisions)):
%o if p == 0: continue
%o if b >= "".join(bp): all_greater = False; break
%o if all_greater: return True
%o return False
%o def a(n): return sum(is5div("".join(b)) for b in product("012", repeat=n))
%o print([a(n) for n in range(1, 10)]) # _Michael S. Branicky_, Aug 28 2021
%Y Cf. A210109, A210324, A210325.
%K nonn,more
%O 1,7
%A _N. J. A. Sloane_, Mar 20 2012
%E a(14)-a(15) from _Michael S. Branicky_, Aug 28 2021
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