

A340914


Square array, read by rows. For n,d >= 0, a(n,d) is the number of congruences of the dtwisted partition monoid of degree n


0



2, 3, 3, 9, 7, 4, 12, 43, 14, 5, 16, 76, 136, 24, 6, 19, 134, 329, 334, 37, 7, 22, 188, 773, 1105, 696, 53, 8, 25, 251, 1281, 3456, 3100, 1294, 72, 9, 28, 323, 1969, 6754, 12806, 7608, 2213, 94, 10, 31, 404, 2864, 11930, 29413, 41054, 16842, 3551, 119, 11, 34, 494, 3993, 19578, 59547, 110312, 117273, 34353, 5419, 147, 12
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OFFSET

0,1


COMMENTS

The dtwisted partition monoids P_{n,d} are defined in the EastRuškuc paper cited below.


REFERENCES

James East and Nik Ruškuc, "Properties of congruences of twisted partition monoids and their lattices", https://arxiv.org/abs/2010.09288


LINKS

Table of n, a(n) for n=0..65.


FORMULA

a(0,d) = d+2,
a(1,d) = (3*d^2+5*d+6)/2,
a(2,d) = (13*d^4+106*d^3+299*d^2+398*d+216)/24,
a(3,d) = (13*d^7+322*d^6+3262*d^5+17920*d^4+58597*d^3+115318*d^2+127128*d+60480)/5040,
a(n,d) = Binomial(3*n+d4,3*n5) + 8*Binomial(3*n+d1,3*n1) +2*Binomial(3*n+d2,3*n1) + 5*Binomial(3*n+d3,3*n1)  2*Binomial(3*n+d4,3*n1) for n >= 4.
For fixed d >= 0, a(n,d) is asymptotic to (3*n)^(d+1) / (d+1)!.
For fixed n >= 4, a(n,d) is asymptotic to 13*d^(3*n1) / (3*n1)!.
A rational generating function is given in the EastRuškuc paper, and also polynomial expressions for a(n,d) with d fixed (and n >= 4).


CROSSREFS

Sequence in context: A209163 A124932 A248788 * A194232 A110042 A306101
Adjacent sequences: A340911 A340912 A340913 * A340915 A340916 A340917


KEYWORD

nonn


AUTHOR

James East, Mar 07 2021


STATUS

approved



