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A062136
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Twelfth column of Losanitsch's triangle A034851 (formatted as lower triangular matrix).
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2
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1, 6, 42, 182, 693, 2184, 6216, 15912, 37854, 83980, 176484, 352716, 676270, 1248072, 2229096, 3863080, 6519591, 10737090, 17299646, 27313650, 42337659, 64512240, 96770544, 143048880, 208616044
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OFFSET
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0,2
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COMMENTS
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Also seventh column (m=6) of triangle A062135.
Number of homeomorphically irreducible (or series-reduced) trees (no vertices of degree 2) with n+9 leaves which become tree P(7) (path on 7 nodes (vertices) or 6 edges (links) when all leaves are omitted. A leave is an edge together with a node of degree 1 at one end. Proof by Polya enumeration. See illustration for A034851.
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LINKS
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Table of n, a(n) for n=0..24.
Index entries for sequences related to trees
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FORMULA
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G.f.: Pe(6, x^2)/((1-x)^(2*6)*(1+x)^6), with Pe(6, x^2) := sum(A034839(6, m)*x^(2*m), m=0..3)= 1+15*x^2+15*x^4+x^6.
a(n) = A034851(n+11,11).
a(2n+1) = A001288(2n+12)/2; a(2n) = (A001288(2n+11)+A000389(n+5))/2. [Gary W. Adamson, Dec 15 2010]
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CROSSREFS
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Cf. A018213.
Sequence in context: A169938 A082986 A180806 * A047663 A054642 A082139
Adjacent sequences: A062133 A062134 A062135 * A062137 A062138 A062139
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang, Jun 19 2001
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STATUS
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approved
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