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

1, 0, 1, 1, 1, 2, 3, 4, 7, 10, 15, 23, 35, 52, 81, 121, 185, 280, 427, 645, 985, 1490, 2269, 3440, 5233, 7936, 12071, 18313, 27839, 42256, 64217, 97490, 148137, 224924, 341725, 518923, 788321, 1197178, 1818597, 2761926, 4195381, 6371808, 9678537, 14699771

Offset: 1

Author

Gus Wiseman, Sep 18 2018

Keywords

• nonn

Comments

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.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..500
• Gus Wiseman, The a(15) = 81 series-reduced palindromic plane trees.

Crossrefs

Cf. A000108, A000670, A001003, A005043, A008965, A025065, A118376, A242414, A317085, A317086, A317087, A319122, A319436.

Programs

Mathematica

srpanplane[n_]:=If[n==1,{{}},Join@@Table[Select[Tuples[srpanplane/@c],#==Reverse[#]&],{c,Join@@Permutations/@Select[IntegerPartitions[n-1],Length[#]>1&]}]];
Table[Length[srpanplane[n]],{n,15}]

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)-x*p); Vec(p)} \\ Andrew Howroyd, Sep 19 2018

Extensions

Terms a(27) and beyond from Andrew Howroyd, Sep 19 2018