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A228178
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The number of boundary edges for all ordered trees with n edges.
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2
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1, 4, 14, 47, 157, 529, 1805, 6238, 21812, 77062, 274738, 987276, 3572568, 13007398, 47617798, 175171543, 647227453, 2400843823, 8937670603, 33380986153, 125045165773, 469700405533, 1768752809221, 6676088636479, 25252913322299, 95712549267151, 363441602176007, 1382467779393307, 5267219868722803
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: (x*C+2*x^2*C^4)/(1-x) where C is the g.f. for the Catalan numbers A000108.
Conjecture: 2*(n+3)*a(n) +2*(-7*n-11)*a(n-1) +(29*n+7)*a(n-2) +(-21*n+19)*a(n-3) +2*(2*n-5)*a(n-4)=0. - R. J. Mathar, Aug 25 2013
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EXAMPLE
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The 5 ordered trees with 3 edges have 3,3,2,3,3 boundary edges with UDUDUD having but 2.
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PROG
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(PARI)
x = 'x + O('x^66);
C = serreverse( x/( 1/(1-x) ) ) / x; \\ Catalan A000108
gf = (x*C+2*x^2*C^4)/(1-x);
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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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