|
%I #15 Nov 16 2021 03:45:20
%S 1,1,2,3,6,10,20,35,68,122,234,426,808,1484,2798,5167,9700,17974,
%T 33656,62498,116826,217236,405646,754938,1408736,2623188,4892848,
%U 9114036,16995110,31664136,59034488,110004243,205068892,382156686,712363344,1327600346,2474618434
%N Number of palindromic plane trees with n nodes.
%C A rooted plane tree is palindromic if the sequence of branches directly under any given node is a palindrome.
%H Andrew Howroyd, <a href="/A319436/b319436.txt">Table of n, a(n) for n = 1..500</a>
%H Gus Wiseman, <a href="/A319436/a319436.png">The a(8) = 35 palindromic plane trees.</a>
%H Gus Wiseman, <a href="/A319436/a319436_1.png">The a(11) = 234 palindromic plane trees.</a>
%F a(n) ~ c * d^n, where d = 1.86383559155190653688720443906758855085492625375... and c = 0.24457511051198663873739022949952908293770055... - _Vaclav Kotesovec_, Nov 16 2021
%e The a(7) = 20 palindromic plane trees:
%e ((((((o)))))) (((((oo))))) ((((ooo)))) (((oooo))) ((ooooo)) (oooooo)
%e ((((o)(o)))) (((o(o)o))) ((o(oo)o)) (o(ooo)o)
%e (((o))((o))) ((o((o))o)) (o((oo))o) (oo(o)oo)
%e (((o)o(o))) ((oo)(oo))
%e (o(((o)))o) ((o)oo(o))
%e ((o)(o)(o)) (o(o)(o)o)
%t panplane[n_]:=If[n==1,{{}},Join@@Table[Select[Tuples[panplane/@c],#==Reverse[#]&],{c,Join@@Permutations/@IntegerPartitions[n-1]}]];
%t Table[Length[panplane[n]],{n,10}]
%o (PARI) PAL(p)={(1+p)/subst(1-p, x, x^2)}
%o seq(n)={my(p=O(1));for(i=1, n, p=PAL(x*p)); Vec(p)} \\ _Andrew Howroyd_, Sep 19 2018
%Y Cf. A000108, A000670, A001003, A005043, A008965, A025065, A032128, A118376, A242414, A317085, A317086, A317087, A319122, A319437.
%K nonn
%O 1,3
%A _Gus Wiseman_, Sep 18 2018
|
