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A340914 Square array, read by rows.  For n,d >= 0, a(n,d) is the number of congruences of the d-twisted 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The d-twisted partition monoids P_{n,d} are defined in the East-Ruškuc 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+d-4,3*n-5) + 8*Binomial(3*n+d-1,3*n-1) +2*Binomial(3*n+d-2,3*n-1) + 5*Binomial(3*n+d-3,3*n-1) - 2*Binomial(3*n+d-4,3*n-1) 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*n-1) / (3*n-1)!.

A rational generating function is given in the East-Ruškuc 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

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Last modified May 8 09:21 EDT 2021. Contains 343666 sequences. (Running on oeis4.)