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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 Joerg Arndt, Table of n, a(n) for n = 0..100 A. Nisnevich, List of entries and lambda terms for n = 1..10 A. Nisnevich, Code to generate list of entries Wikipedia, Lambda calculus: Notation 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 Adjacent sequences:  A260658 A260659 A260660 * A260662 A260663 A260664 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 August 11 15:10 EDT 2022. Contains 356066 sequences. (Running on oeis4.)