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Number of rigid hypergroups of order n.
3

%I #25 Aug 09 2024 10:07:16

%S 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,

%T 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,

%U 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6

%N Number of rigid hypergroups of order n.

%C 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

%C Also decimal expansion of 19/15. - _Stefano Spezia_, Mar 23 2022

%D R. Bayon and N. Lygeros, Hyperstructures and Automorphism Groups, submitted.

%D F. Marty, Sur une généralisation de la notion de groupe. In Proc. 8th Congr. des Mathématiciens Scandinaves, Stockholm, pp. 45-49, 1934.

%D Th. Vougiouklis, The fundamental relation in hyperrings: The general hyperfield, Fourth Int. Congress Algebraic Hyperstructures and Appl. (AHA), 1991, pp. 203-211.

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).

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

%F G.f.: x*(1 + x + 4*x^2)/(1 - x). - _Stefano Spezia_, Mar 23 2022

%F E.g.f.: 6*exp(x) - 6 - 5*x - 2*x^2. - _Elmo R. Oliveira_, Aug 09 2024

%t Array[If[# <= 2, #, 6] &, 105] (* _Michael De Vlieger_, Dec 01 2019 *)

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

%K nonn,easy

%O 1,2

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