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A052702
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A simple context-free grammar.
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3
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0, 0, 0, 0, 1, 2, 3, 6, 13, 26, 52, 108, 226, 472, 993, 2106, 4485, 9586, 20576, 44332, 95814
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| Contribution from Paul Barry (pbarry(AT)wit.ie), May 24 2009: (Start)
Hankel transform of A052702 is A160705. Hankel transform of A052702(n+1) is A160706.
Hankel transform of A052702(n+2) is -A131531(n+1). Hankel transform of A052702(n+3) is A160706(n+5).
Hankel transform of A052702(n+4) is A160705(n+5). (End)
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 654
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FORMULA
| G.f.: (1/2)/x^2*(1-x-(1-2*x+x^2-4*x^3)^(1/2))-(1/2)/x*(1-x-(1-2*x+x^2-4*x^3)^(1/2))-x
Recurrence: {a(1)=0, a(2)=0, a(4)=1, a(3)=0, a(6)=3, a(7)=6, a(5)=2, (-2+4*n)*a(n)+(-7-5*n)*a(n+1)+(8+3*n)*a(n+2)+(-13-3*n)*a(n+3)+(n+6)*a(n+4)}
Contribution from Paul Barry (pbarry(AT)wit.ie), May 24 2009: (Start)
G.f.: (1-2x+x^2-2x^3-(1-x)*sqrt(1-2x+x^2-4x^3))/(2x^2).
a(n+1)=sum{k=0..n-1, C(n-k-1,2k-1)*A000108(k)}. (End)
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MAPLE
| spec := [S, {B=Prod(C, Z), S=Prod(B, B), C=Union(S, B, Z)}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
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CROSSREFS
| Sequence in context: A086514 A079662 A007910 * A058766 A127601 A030038
Adjacent sequences: A052699 A052700 A052701 * A052703 A052704 A052705
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KEYWORD
| easy,nonn
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AUTHOR
| encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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