A134201 Number of rigid hypergroups of order n.

1, 2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

Offset: 1

Author

Roman Bayon (roman.bayon(AT)gmail.com), Oct 14 2007

Keywords

• nonn
• easy

Comments

a(n) is also the number of I-toothpicks added to the structure of the cellular automaton of A323646 when starts its n-th cycle. Column 1 of triangle A323647. - Omar E. Pol, Nov 25 2019

Also decimal expansion of 19/15. - Stefano Spezia, Mar 23 2022

References

• R. Bayon and N. Lygeros, Hyperstructures and Automorphism Groups, submitted.
• F. Marty, Sur une généralisation de la notion de groupe. In Proc. 8th Congr. des Mathématiciens Scandinaves, Stockholm, pp. 45-49, 1934.
• Th. Vougiouklis, The fundamental relation in hyperrings: The general hyperfield, Fourth Int. Congress Algebraic Hyperstructures and Appl. (AHA), 1991, pp. 203-211.

Links

• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Cf. A108089, A132590, A134202, A323646, A323647.

Programs

Mathematica

Array[If[# <= 2, #, 6] &, 105] (* Michael De Vlieger, Dec 01 2019 *)

Formula

a(1) = 1, a(2) = 2, a(n) = 6 for n > 2.

G.f.: x*(1 + x + 4*x^2)/(1 - x). - Stefano Spezia, Mar 23 2022

E.g.f.: 6*exp(x) - 6 - 5*x - 2*x^2. - Elmo R. Oliveira, Aug 09 2024