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Search: id:A094365
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| A094365 |
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Number of numerical semigroups with three nonextraneous generators and Frobenius number n. |
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+0
3
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| 0, 1, 0, 1, 1, 1, 3, 2, 3, 4, 4, 1, 9, 7, 4, 7, 11, 5, 14, 6, 8, 16, 17, 2, 17, 15, 17, 10, 24, 6, 29, 12, 29, 23, 24, 5, 46, 29, 26, 12, 42, 11, 53, 19, 34, 40, 53, 10, 55, 24, 42, 30, 72, 16, 46, 23, 55, 46, 70, 7, 96, 46, 51, 34, 63, 21, 108, 43, 80, 40, 88, 11, 117, 49, 60
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OFFSET
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1,7
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COMMENT
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A numerical semigroup is a set of natural numbers closed under addition. Its Frobenius number is the largest number not in it.
A generator is extraneous if it can be generated by other generators.
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REFERENCES
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J. L. Davison, On the linear Diophantine problem of Frobenius numbers, J. Number Theory 48 (1994), p353-363.
J. C. Rosales and M. B. Branco, Irreducible numerical semigroups, Pacific Journal Mathematics, 2003, No. 1.
J. C. Rosales, P. A. Garcia-Sanchez and J. I. Garcia-Garcia, Every positive integer is the Frobenius number of a numerical semigroup with three generators, Math. Scand. 94 (2004), no. 1, 5-12.
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EXAMPLE
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a(7)=3 because are three such semigroups with Frobenius number 7. Their complements (and a generating triple) are {1,2,3,7} (4,5,6); {1,2,4,5,7} (3,8,10); {1,2,3,6,7} (4,5,11).
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CROSSREFS
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Cf. A094366 (2 generators), A094367 (3 generators).
Sequence in context: A093407 A147658 A105161 this_sequence A098822 A131597 A077070
Adjacent sequences: A094362 A094363 A094364 this_sequence A094366 A094367 A094368
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KEYWORD
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nonn
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AUTHOR
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Kaye A. Archer (godchaser_2(AT)hotmail.com), May 06 2004
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EXTENSIONS
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Edited by Don Reble (djr(AT)nk.ca), Apr 26 2007
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