OFFSET
0,2
COMMENTS
An idempotent monoid satisfies the equation xx=x for any element x.
A squarefree word may be equivalent to a smaller or larger word as a consequence of the idempotent equation.
REFERENCES
M. Lothaire, Combinatorics on Words. Addison-Wesley, Reading, MA, 1983, p. 32.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Morgan Rogers, From free idempotent monoids to free multiplicatively idempotent rigs, arXiv:2408.17440 [math.RA], 2024. See pp. 21, 23.
Eric Weisstein's World of Mathematics, Monoid.
Eric Weisstein's World of Mathematics, Free Idempotent Monoid
FORMULA
a(n) = Sum_{k=0..n} (C(n, k) Prod_{i=1..k} (k-i+1)^(2^i)).
Binomial transform of A030450. - Michael Somos, Oct 22 2006
MATHEMATICA
Array[Sum[Binomial[#, k]* Product[(k - i + 1)^(2^i), {i, k}], {k, 0, #}] &, 10, 0] (* Michael De Vlieger, Sep 05 2024 *)
PROG
(PARI) {a(n)=sum(k=0, n, binomial(n, k)*prod(i=1, k, (k-i+1)^2^i))} /* Michael Somos, Oct 22 2006 */
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
One more term from Gabriel Cunningham (gcasey(AT)mit.edu), Nov 14 2004
STATUS
approved