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A243771
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Number of Dyck paths of semilength n having exactly two (possibly overlapping) occurrences of the consecutive step pattern given by the binary expansion of n, where 1=U=(1,1) and 0=D=(1,-1).
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3
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1, 1, 2, 12, 69, 98, 180, 1056, 3967, 18357, 77685, 264563, 1245762, 1915056, 5303208, 24548040, 107835695, 375494210, 1898502240, 4942470942, 23489565822, 104559681798, 413327570240, 1426320927138, 6025235528016, 19911812844324, 87316285518504
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OFFSET
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2,3
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LINKS
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EXAMPLE
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a(2) = 1: (UD)[UD].
a(3) = 1: (U[U)U]DDD.
a(4) = 2: U(UDD)U[UDD], UU(UDD)[UDD].
a(5) = 12: (UD[U)DU]UDDUD, (UD[U)DU]UUDDD, (UDU)UDD[UDU]D, (UDU)[UDU]DDUD, (UDU)[UDU]UDDD, (UDU)U[UDU]DDD, UUDD(UD[U)DU]D, U(UDU)DD[UDU]D, U(UD[U)DU]DDUD, U(UD[U)DU]UDDD, U(UDU)[UDU]DDD, UU(UD[U)DU]DDD.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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