login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A319436 Number of palindromic plane trees with n nodes. 10
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
A rooted plane tree is palindromic if the sequence of branches directly under any given node is a palindrome.
LINKS
FORMULA
a(n) ~ c * d^n, where d = 1.86383559155190653688720443906758855085492625375... and c = 0.24457511051198663873739022949952908293770055... - Vaclav Kotesovec, Nov 16 2021
EXAMPLE
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)
MATHEMATICA
panplane[n_]:=If[n==1, {{}}, Join@@Table[Select[Tuples[panplane/@c], #==Reverse[#]&], {c, Join@@Permutations/@IntegerPartitions[n-1]}]];
Table[Length[panplane[n]], {n, 10}]
PROG
(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
CROSSREFS
Sequence in context: A030436 A030227 A180272 * A061551 A026034 A178381
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 18 2018
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)