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A256120 Number of tautologies in propositional calculus of length n. 2
0, 0, 0, 0, 2, 2, 12, 6, 57, 88, 373, 554, 2086 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

a(n) is the number of tautologies that are n symbols long in propositional calculus with the connectives not (~), and (*), or (+), implies (->) and if and only if (<->).

When measuring the length of a tautology, all brackets must be included. The connectives -> and <-> are counted as one symbol each (but writing them as such requires non-ASCII characters).

Formally, the language used for this sequence contains the symbols a-z and A-Z (the variables),~,*,+,->,<->,( and ).

The formulas are defined by the following rules:

* Every variable is a formula.

* If A is a formula, then ~A is a formula.

* If A and B are formulas, then (A*B), (A+B), (A->B) and (A<->B) are all formulas.

A formula is a tautology if it is true for any assignment of truth values to the variables.

LINKS

Table of n, a(n) for n=1..13.

M. Scroggs, Logic Bot, pt. 2

M. Scroggs, List of tautologies

EXAMPLE

The tautologies of length 5 are (a->a) and (a<->a).

The tautologies of length 6 are (~a+a) and (a+~a).

The tautologies of length 7 are (~~a->a), (~~a<->a), (~a->~a), (~a<->~a), (a->~~a), (a<->~~a), ~(~a<->a), ~(~a*a), ~(a<->~a), ~(a*~a), ~~(a->a) and ~~(a<->a).

CROSSREFS

Cf. A277275, A277276

Sequence in context: A073768 A278534 A096855 * A024538 A279879 A279139

Adjacent sequences:  A256117 A256118 A256119 * A256121 A256122 A256123

KEYWORD

nonn,more

AUTHOR

Matthew Scroggs, Mar 15 2015

EXTENSIONS

More terms from Matthew Scroggs, Mar 27 2015

Typo in a(11) corrected by Matthew Scroggs, Mar 27 2015

STATUS

approved

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Last modified August 21 08:43 EDT 2019. Contains 326162 sequences. (Running on oeis4.)