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A000781
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a(n) = 3*Catalan(n) - Catalan(n-1) - 1.
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1
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1, 4, 12, 36, 111, 353, 1154, 3860, 13155, 45525, 159561, 565249, 2020687, 7280419, 26410094, 96378164, 353576699, 1303271309, 4824150869, 17925098069, 66834680639, 249981423899, 937696277309, 3526652828321, 13295935057031, 50240112815003
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: (1/2)*(((sqrt(1-4*x)-7)*x - 3*sqrt(1-4*x) + 3)/x^2 + 2/(x-1)). - Harvey P. Dale, Apr 28 2013
Conjecture: 3*(n+1)*a(n) + (-19*n+7)*a(n-1) + (33*n-53)*a(n-2) + (-21*n+61)*a(n-3) + 2*(2*n-9)*a(n-4) = 0. - R. J. Mathar, Aug 20 2013
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MATHEMATICA
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3#[[2]]-#[[1]]-1&/@Partition[CatalanNumber[Range[0, 30]], 2, 1] (* Harvey P. Dale, Apr 28 2013 *)
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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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