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A346757
a(n) is the number of arches with a length of one and exactly one covering arch for semi-meanders with n top arches.
0
0, 2, 2, 12, 20, 88, 180, 716, 1648, 6244, 15512, 57188, 149892, 543324, 1481636, 5310764, 4930380, 53102508, 152935148, 540918660, 1588618212, 5595773136, 16701973552
OFFSET
2,2
COMMENTS
The ratio of the number of semi-meanders in generation n+1 to the number of semi-meanders in generation n is equal to the ratio of the differences of these semi-meander subset arch sequences in successive generations.
A000682(n+1)/A000682(n) = (A260785(n+3) - a(n+1))/(A260785(n+2) - a(n)).
REFERENCES
See A000682.
LINKS
P. Di Francesco, O. Golinelli and E. Guitter, Meanders: exact asymptotics, arXiv:cond-mat/9910453 [cond-mat.stat-mech], 1999-2000; Nuclear Physics B, volume 570, issue 3, 27 March 2000, 699-712.
FORMULA
For n >= 2, a(n) = A260785(n+2) - 2*A000682(n).
EXAMPLE
n = 5, || indicates an arch of length one with exactly one covering arch.
/\ /\ /\
/\ //\\ //\\ /\ /\ /\ /\ /\ / \
//\\ ///\\\ ///\\\ //\\ /\ //\\ //\\ //\\ //\\ /\ /\ /\ //\/\\
|| || || || || || ||||
/\ /\
/ \ / \ /\
//\ \ / /\\ / \
///\\/\\ /\ /\ //\//\\\ //\/\\ /\ /\
|| || |||| a(5) = 12.
CROSSREFS
Sequence in context: A054916 A194767 A302368 * A202669 A178845 A140431
KEYWORD
nonn,more
AUTHOR
Roger Ford, Aug 01 2021
STATUS
approved