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%I #21 Jun 12 2017 08:33:57
%S 0,0,5,168,659,163,14,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N Number of strings of n digits from 1..9 such that a formula using the single digits in the given order with result 0 needs at least one division.
%C For definitions see A288350. An exhaustive computation for the 9^8 strings of 8 digits confirms that for all of them formulas avoiding divisions exist. a(8) = 0 implies that a(n) = 0 for n > 8.
%e a(3)=5, because the 5 3-digit strings 263 (0=2-6/3), 284 (0=2-8/4), 362 (0=3-6/2), 393 (3-9/3), 482 (0=4-8/2) are the only ones of the 9^3-A288351(3)=274 3-digit strings for which a formula with result 0 exists that cannot avoid including a division.
%e A288502 provides a list of all strings with this property.
%Y Cf. A288350, A288351, A288502, A288550.
%K nonn
%O 1,3
%A _Hugo Pfoertner_, Jun 10 2017
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