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Search: id:A086625
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| 1, 2, 3, 6, 12, 26, 59, 138, 332, 814, 2028, 5118, 13054, 33598, 87143, 227542, 597640, 1577866, 4185108, 11146570, 29798682, 79932298, 215072896, 580327122, 1569942098, 4257254850, 11569980794, 31508150890, 85968266198, 234975421554
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) is the number of Dyck (n+1)-paths (A000108) containing no DUDD and no UUPDD where P is a nonempty Dyck subpath. Example: a(2)=3 counts UUDDUD, UDUUDD, UDUDUD but omits UUUDDD because it contains an offending UUPDD and omits UUDUDD because it contains a DUDD. - David Callan (callan(AT)stat.wisc.edu), Oct 26 2006
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FORMULA
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G.f.: A(x) = (1-x^2)/(1-x)^2 + x^2*A(x)^2.
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CROSSREFS
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Cf. A086623 (table), A086624 (diagonal).
Sequence in context: A052523 A166296 A151527 this_sequence A152172 A001677 A024422
Adjacent sequences: A086622 A086623 A086624 this_sequence A086626 A086627 A086628
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jul 24 2003
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