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A262301 Number of normal linear lambda terms of size n with no free variables. 6
1, 3, 26, 367, 7142, 176766, 5304356, 186954535, 7566084686, 345664350778, 17592776858796, 986961816330662, 60502424162842876, 4023421969420255644, 288464963899330354104, 22180309834307193611287, 1820641848410408158704734, 158897008602951290424279330 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Gheorghe Coserea, Table of n, a(n) for n = 1..100

Paul Tarau, Valeria de Paiva, Deriving Theorems in Implicational Linear Logic, Declaratively, arXiv:2009.10241 [cs.LO], 2020. See also Github, (2020).

Noam Zeilberger, Counting isomorphism classes of beta-normal linear lambda terms, arXiv:1509.07596 [cs.LO], 2015.

Wikipedia, Lambda calculus

FORMULA

A(x) = F(x,0), where A(x) = Sum_{n>=1} a(n)*x^n and F(x,t) satisfies F = x*t/(1-F) + deriv(F,t), with F(0,t)=0, deriv(F,x)(0,t)=1+t. - Gheorghe Coserea, Apr 01 2017

EXAMPLE

A(x) = x + 3*x^2 + 26*x^3 + 367*x^4 + 7142*x^5 + ...

MATHEMATICA

terms = 18; F[_, _] = 0;

Do[F[x_, t_] = Series[x t/(1-F[x, t]) + D[F[x, t], t], {x, 0, terms}, {t, 0, terms}] // Normal, {2 terms}];

CoefficientList[F[x, 0], x][[2 ;; terms+1]] (* Jean-Fran├žois Alcover, Sep 02 2018, after Gheorghe Coserea *)

PROG

(PARI)

F(N) = {

  my(x='x+O('x^N), t='t, F0=x, F1=0, n=1);

  while(n++,

    F1 = x*t/(1-F0) + deriv(F0, t);

    if (F1 == F0, break()); F0 = F1; );

  F0;

};

seq(N) = Vec(subst(F(N+1), 't, 0));

seq(18) \\ Gheorghe Coserea, Apr 01 2017

CROSSREFS

Column 0 of A318110.

Cf. A062980, A267827.

Sequence in context: A328269 A136046 A206404 * A317654 A143155 A300283

Adjacent sequences:  A262298 A262299 A262300 * A262302 A262303 A262304

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Sep 30 2015

EXTENSIONS

More terms from Gheorghe Coserea, Apr 01 2017

STATUS

approved

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Last modified January 19 00:22 EST 2022. Contains 350464 sequences. (Running on oeis4.)