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A260661 The number of distinct (up to alpha-equivalence) closed lambda calculus terms n characters long, assuming standard notational conventions. 1
0, 0, 0, 0, 1, 3, 8, 22, 68, 235, 896, 3700, 16388, 77424, 388337, 2058898, 11494391, 67345463, 412884769, 2641957682, 17603708949, 121891857559, 875463364581, 6511352351724, 50074591410942, 397627804820554, 3256109939552809, 27464891261741533, 238366531369343096, 2126510299723649140, 19482346640311421722, 183143139819128271540, 1765079515780983078401 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,6
COMMENTS
"Standard notational conventions" here means that "lambda a.lambda b.M" must be simplified to "lambda ab.M", "(MN)" must be simplified to "MN", and "(MN)P" must be simplified to "MNP" (see the Wikipedia article for more details).
LINKS
EXAMPLE
For n=6, the a(6)=8 terms are: lambda a.aaa, lambda ab.aa, lambda ab.ab, lambda ab.ba, lambda ab.bb, lambda abc.a, lambda abc.b, lambda abc.c.
PROG
(Sage)
def a(n):
return term(n, 0, 0, 0)
@CachedFunction
def term(n, k, L, R):
return var(n, k) + lam(n-2 if R else n, k) + app(n-2 if L else n, k, R and not L)
def var(n, k):
return k if n==1 else 0
@CachedFunction
def lam(n, k):
return sum(var(n-v-2, k+v) + app(n-v-2, k+v, 0) for v in range(1, n-2))
@CachedFunction
def app(n, k, R):
return sum(term(u, k, 0, 1) * term(n-u, k, 1, R) for u in range(1, n))
# (See Jacobs link for more details.) Alex Nisnevich, Jun 03 2016
CROSSREFS
Sequence in context: A000732 A092090 A011958 * A171841 A233449 A148770
KEYWORD
nonn
AUTHOR
Alex Nisnevich, Nov 13 2015
EXTENSIONS
Corrected a(10) and more terms added by Alex Nisnevich, Jun 03 2016
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)