

A319608


Irregular triangle read by rows: T(n,k) is the number of irreducible numerical semigroups with Frobenius number n and k minimal generators less than n/2.


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1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 4, 1, 1, 1, 1, 5, 2, 1, 4, 1, 1, 4, 2, 1, 4, 2, 1, 7, 6, 1, 1, 4, 2, 1, 8, 9, 2, 1, 5, 4, 1, 1, 7, 8, 2, 1, 8, 9, 2, 1, 10, 17, 7, 1, 1, 5, 6, 2, 1, 10, 19, 12, 2, 1, 10, 16, 7, 1, 1, 10, 21, 11, 2, 1, 9, 16, 9, 2, 1, 13, 34, 26, 8, 1, 1, 8, 15, 10, 2, 1, 14, 41, 37, 14, 2
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OFFSET

1,9


COMMENTS

The length of each row is floor((n+1)/2)  floor(n/3).
The expected number of minimal generators of a randomly selected numerical semigroup S(M,p) equals Sum_{n=1..M} ( p * (1  p)^(floor(n/2)) * Product_{k>=0} T(n,k)*p^k ).


LINKS



EXAMPLE

T(13,2) = 2, since {5,6,9} and {7,8,9,10,11,12} minimally generate irreducible numerical semigroups with Frobenius number 13.
When written in rows:
1
1
1
1
1, 1
1
1, 2
1, 1
1, 2
1, 2
1, 4, 1
1, 1
1, 5, 2
1, 4, 1
1, 4, 2
1, 4, 2
1, 7, 6, 1
1, 4, 2
1, 8, 9, 2
1, 5, 4, 1
1, 7, 8, 2
1, 8, 9, 2
1, 10, 17, 7, 1
1, 5, 6, 2
1, 10, 19, 12, 2
1, 10, 16, 7, 1
1, 10, 21, 11, 2
1, 9, 16, 9, 2
1, 13, 34, 26, 8, 1
1, 8, 15, 10, 2


CROSSREFS



KEYWORD

nonn,tabf


AUTHOR



STATUS

approved



