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A319436
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Number of palindromic plane trees with n nodes.
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10
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1, 1, 2, 3, 6, 10, 20, 35, 68, 122, 234, 426, 808, 1484, 2798, 5167, 9700, 17974, 33656, 62498, 116826, 217236, 405646, 754938, 1408736, 2623188, 4892848, 9114036, 16995110, 31664136, 59034488, 110004243, 205068892, 382156686, 712363344, 1327600346, 2474618434
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OFFSET
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1,3
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COMMENTS
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A rooted plane tree is palindromic if the sequence of branches directly under any given node is a palindrome.
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LINKS
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FORMULA
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a(n) ~ c * d^n, where d = 1.86383559155190653688720443906758855085492625375... and c = 0.24457511051198663873739022949952908293770055... - _Vaclav Kotesovec_, Nov 16 2021
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EXAMPLE
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The a(7) = 20 palindromic plane trees:
((((((o)))))) (((((oo))))) ((((ooo)))) (((oooo))) ((ooooo)) (oooooo)
((((o)(o)))) (((o(o)o))) ((o(oo)o)) (o(ooo)o)
(((o))((o))) ((o((o))o)) (o((oo))o) (oo(o)oo)
(((o)o(o))) ((oo)(oo))
(o(((o)))o) ((o)oo(o))
((o)(o)(o)) (o(o)(o)o)
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MATHEMATICA
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panplane[n_]:=If[n==1, {{}}, Join@@Table[Select[Tuples[panplane/@c], #==Reverse[#]&], {c, Join@@Permutations/@IntegerPartitions[n-1]}]];
Table[Length[panplane[n]], {n, 10}]
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PROG
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(PARI) PAL(p)={(1+p)/subst(1-p, x, x^2)}
seq(n)={my(p=O(1)); for(i=1, n, p=PAL(x*p)); Vec(p)} \\ _Andrew Howroyd_, Sep 19 2018
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CROSSREFS
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Cf. A000108, A000670, A001003, A005043, A008965, A025065, A032128, A118376, A242414, A317085, A317086, A317087, A319122, A319437.
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KEYWORD
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nonn
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AUTHOR
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_Gus Wiseman_, Sep 18 2018
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STATUS
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approved
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