A321571 a(n) is the order of the free linear Heyting algebra on n generators.

2, 6, 342, 137186159382, 20574018325197218999594988949603700627255750813932694467611442806

Offset

1,1

Comments

a(7) has 4016 digits and so is too long to be included. - Miles Englezou, Mar 08 2026

Links

Miles Englezou, Table of n, a(n) for n = 1..6

Peter Freyd, On the size of Heyting Semi-Lattices and Equationally Linear Heyting Algebras, Jul 17 2017.

Formula

a(n) = (b(n-1) + 1)*b(n-1), where b(n) = Product_{r=0..n-1} (b(r) + 1)^binomial(n,r). - Miles Englezou, Mar 08 2026

Prog

(PARI) a(n) = (b(n) = prod(r = 0, n-1, (1+b(r))^binomial(n, r))); (b(n-1)+1)*b(n-1) \\ Miles Englezou, Mar 08 2026

Crossrefs

Cf. A050318, A050365, A067765.

Sequence in context: A215293 A264410 A135014 * A092024 A252741 A389994

Adjacent sequences: A321568 A321569 A321570 * A321572 A321573 A321574

Keyword

nonn

Author

Peter Luschny, Nov 13 2018

Extensions

a(5) added by Miles Englezou, Mar 08 2026

Status

approved