cp's OEIS Frontend

A220471 Number of closed simply typable lambda-terms of size n with size 0 for the variables.

%I A220471 #59 Nov 23 2020 09:57:40
%S A220471 1,2,9,40,238,1564,11807,98529,904318,9006364,96709332,1110858977,
%T A220471 13581942434,175844515544
%N A220471 Number of closed simply typable lambda-terms of size n with size 0 for the variables.
%C A220471 Typable terms are terms that satisfy constraints which make them well formed.
%C A220471 The current computation requires one to generate all the plain lambda terms and to sieve out those that are typable.  This is feasible for the 63782411 terms of size 10 but not for the 851368766 terms of size 11.
%D A220471 Alonzo Church, A Formulation of the Simple Theory of Types, J. Symb. Log. 5(2): 56-68 (1940).
%H A220471 Katarzyna Grygiel and Pierre Lescanne, <a href="http://arxiv.org/abs/1210.2610">Counting and generating lambda-terms</a>, arXiv preprint arXiv:1210.2610, 2012
%H A220471 Paul Tarau, <a href="http://www.cse.unt.edu/~tarau/research/2015/xco.pdf">On a Uniform Representation for Combinators, Arithmetic, Lambda Terms and Types</a>, preprint, 2015.
%H A220471 Paul Tarau, <a href="http://www.cse.unt.edu/~tarau/research/2015/dbt.pdf">On Type-directed Generation of Lambda Terms</a>, preprint, 2015.
%H A220471 Paul Tarau, <a href="http://www.cse.unt.edu/~tarau/research/2015/dbx.pdf">On logic programming representations of lambda terms: de Bruijn indices, compression, type inference, combinatorial generation, normalization</a>, 2015.
%H A220471 P. Tarau, <a href="http://arxiv.org/abs/1507.06944">A Logic Programming Playground for Lambda Terms, Combinators, Types and Tree-based Arithmetic Computations</a>, arXiv preprint arXiv:1507.06944, 2015
%H A220471 Paul Tarau, <a href="https://doi.org/10.1007/978-3-319-20615-8_8">"Ranking/unranking of lambda terms with compressed de Bruijn indices</a>, CICM 2015, Lect. Not. Comp. Sci. 9140, p. 118-133
%H A220471 Paul Tarau, A Hiking Trip Through the Orders of Magnitude: Deriving Efficient Generators for Closed Simply-Typed Lambda Terms and Normal Forms, arXiv preprint arXiv:1608.03912, 2016
%Y A220471 Cf. A220894.
%K A220471 nonn,more
%O A220471 1,2
%A A220471 _Pierre Lescanne_, Apr 10 2013
%E A220471 a(11) and a(12) added from Tarau (arXiv:1507.06944, 2015). - _N. J. A. Sloane_, Jan 30 2016
%E A220471 a(13) and a(14) added from Tarau (2016). - _N. J. A. Sloane_, Aug 04 2017