cp's OEIS Frontend

A319437 Number of series-reduced palindromic plane trees with n nodes.

%I A319437 #8 Sep 19 2018 15:12:14
%S A319437 1,0,1,1,1,2,3,4,7,10,15,23,35,52,81,121,185,280,427,645,985,1490,
%T A319437 2269,3440,5233,7936,12071,18313,27839,42256,64217,97490,148137,
%U A319437 224924,341725,518923,788321,1197178,1818597,2761926,4195381,6371808,9678537,14699771
%N A319437 Number of series-reduced palindromic plane trees with n nodes.
%C A319437 A rooted plane tree is series-reduced if every non-leaf node has at least two branches, and palindromic if the sequence of branches directly under any given node is a palindrome.
%H A319437 Andrew Howroyd, <a href="/A319437/b319437.txt">Table of n, a(n) for n = 1..500</a>
%H A319437 Gus Wiseman, <a href="/A319437/a319437.png">The a(15) = 81 series-reduced palindromic plane trees.</a>
%t A319437 srpanplane[n_]:=If[n==1,{{}},Join@@Table[Select[Tuples[srpanplane/@c],#==Reverse[#]&],{c,Join@@Permutations/@Select[IntegerPartitions[n-1],Length[#]>1&]}]];
%t A319437 Table[Length[srpanplane[n]],{n,15}]
%o A319437 (PARI) PAL(p)={(1+p)/subst(1-p, x, x^2)}
%o A319437 seq(n)={my(p=O(1));for(i=1, n, p=PAL(x*p)-x*p); Vec(p)} \\ _Andrew Howroyd_, Sep 19 2018
%Y A319437 Cf. A000108, A000670, A001003, A005043, A008965, A025065, A118376, A242414, A317085, A317086, A317087, A319122, A319436.
%K A319437 nonn
%O A319437 1,6
%A A319437 _Gus Wiseman_, Sep 18 2018
%E A319437 Terms a(27) and beyond from _Andrew Howroyd_, Sep 19 2018