A288352 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.

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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,3

Comments

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.

Links

Table of n, a(n) for n=1..80.

Example

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.
A288502 provides a list of all strings with this property.

Crossrefs

Cf. A288350, A288351, A288502, A288550.

Sequence in context: A229414 A210923 A229524 * A301949 A316709 A293953

Adjacent sequences: A288349 A288350 A288351 * A288353 A288354 A288355

Keyword

nonn

Author

Hugo Pfoertner, Jun 10 2017

Status

approved