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A262301
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Number of normal linear lambda terms of size n with no free variables.
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6
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1, 3, 26, 367, 7142, 176766, 5304356, 186954535, 7566084686, 345664350778, 17592776858796, 986961816330662, 60502424162842876, 4023421969420255644, 288464963899330354104, 22180309834307193611287, 1820641848410408158704734, 158897008602951290424279330
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OFFSET
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1,2
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LINKS
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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
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FORMULA
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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
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EXAMPLE
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A(x) = x + 3*x^2 + 26*x^3 + 367*x^4 + 7142*x^5 + ...
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MATHEMATICA
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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-François Alcover, Sep 02 2018, after Gheorghe Coserea *)
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PROG
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(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
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CROSSREFS
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Column 0 of A318110.
Cf. A062980, A267827.
Sequence in context: A328269 A136046 A206404 * A317654 A143155 A300283
Adjacent sequences: A262298 A262299 A262300 * A262302 A262303 A262304
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Sep 30 2015
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EXTENSIONS
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More terms from Gheorghe Coserea, Apr 01 2017
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STATUS
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approved
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