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Search: id:A005345
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| A005345 |
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Number of elements of a free idempotent monoid on n letters.
(Formerly M1820)
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+0
3
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| 1, 2, 7, 160, 332381, 2751884514766, 272622932796281408879065987, 3641839910835401567626683593436003894250931310990279692, 84883186791383076098667112629300091811829763518160024883948061425505953907813622\ 1019132415247551725144817958905
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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An idempotent monoid satisfies the equation xx=x for any element x.
A square-free word may be equivalent to a smaller or larger word as a consequence of the idempotent equation.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
M. Lothaire, Combinatorics on Words. Addison-Wesley, Reading, MA, 1983, p. 32.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Free Idempotent Monoid
Index entries for sequences related to monoids
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FORMULA
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a(n) = Sum C(n, k) Prod (k-i+1)^(2^i), i=1..k; k=0..n.
Binomial transform of A030450. - Michael Somos Oct 22 2006
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PROGRAM
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(PARI) {a(n)=sum(k=0, n, binomial(n, k)*prod(i=1, k, (k-i+1)^2^i))} /* Michael Somos Oct 22 2006 */
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CROSSREFS
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A030449(n)=a(n)-1.
Sequence in context: A101799 A062617 A064607 this_sequence A077746 A159034 A120381
Adjacent sequences: A005342 A005343 A005344 this_sequence A005346 A005347 A005348
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jeffrey Shallit
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EXTENSIONS
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One more term from Gabriel Cunningham (gcasey(AT)mit.edu), Nov 14 2004
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