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A125625
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Number of elements in the semigroup of type K_n.
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0
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1, 2, 5, 18, 115, 1710, 83973, 22263378, 64146328635, 5387481983035854, 53332505278384935836485, 448356696524549059043145139274042, 52321110785739610206886887435107004491768788251, 4402157583106925818769478699470667613674438846830415891359277374958, 71336346872409035510345323533390649100576348044074421590685110464047512124710404684631077386973
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OFFSET
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0,2
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COMMENTS
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The semigroup K_3 with 3 generators occurs in convexity theory; K_n is the generic semigroup with n generators.
In the paper of Kudryavtseva and Mazorchuk it is shown that the n-th term of this sequence gives the number of words in the alphabet 1,2,...,n such that between any repetitions of any letter there must occur both a smaller and a bigger letter (in the natural order). For example, the word 2132 is allowed while 3213 is not. [V. Mazorchuk, Aug 24 2011]
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REFERENCES
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Alsaody, S. (2007). "Determining the Elements of a Semigroup." Uppsala, Sweden: Dept. Of Mathematics, Uppsala University, Report No. 2007:3.
Kiselman, C. O. (2002). "A Semigroup of Operators in Convexity Theory." Trans. Am, Math. Soc., 354, No. 5, pp. 2035-2053.
G. Kudryavtseva and V. Mazorchuk; On Kiselman's semigroup, Preprint Uppsala University 2005, published in: Yokohama Math. J. 55 (2009), no.1, 21-46.
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LINKS
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Table of n, a(n) for n=0..14.
L. Forsberg, Effective representations of Hecke-Kiselman monoids of type A, arXiv preprint arXiv:1205.0676, 2012. - From N. J. A. Sloane, Oct 13 2012
M. Selin, Source code (C++) for algorithm.
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PROG
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(Magma) /* program for a(6) */ F<a, b, c, d, e, f> := FreeMonoid(6); Q<a, b, c, d, e, f> := quo< F | a^2 = a, b^2 = b, c^2 = c, d^2 = d, e^2 = e, f^2 = f, a*b*a = b*a*b = a*b, a*c*a = c*a*c = a*c, a*d*a = d*a*d = a*d, a*e*a = e*a*e = a*e, a*f*a = f*a*f = a*f, b*c*b = c*b*c = b*c, b*d*b = d*b*d = b*d, b*e*b = e*b*e = b*e, b*f*b = f*b*f = b*f, c*d*c = d*c*d = c*d, c*e*c = e*c*e = c*e, c*f*c = f*c*f = c*f, d*e*d = e*d*e = d*e, d*f*d = f*d*f = d*f, e*f*e = f*e*f = e*f >; M<a, b, c, d, e, f> := RWSMonoid(Q); Order(M); /* Klaus Brockhaus, Mar 02 2007 */
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CROSSREFS
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Sequence in context: A005805 A058338 A006896 * A281532 A097584 A197855
Adjacent sequences: A125622 A125623 A125624 * A125626 A125627 A125628
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KEYWORD
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nonn
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AUTHOR
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Seidon Alsaody (Seidon.Alsaody.5527(AT)student.uu.se), Jan 27 2007
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EXTENSIONS
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a(6) from Klaus Brockhaus, Mar 02 2007
More terms from M. Selin (mxrten(AT)kth.se), Jan 16 2008, Jan 25 2008
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STATUS
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approved
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