login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A052471 Number of noncaterpillar trees on n nodes (A000055-A005418). 2
0, 0, 0, 0, 0, 0, 1, 3, 11, 34, 99, 279, 773, 2103, 5661, 15160, 40373, 107355, 285059, 757273, 2013177, 5361100, 14303274, 38250297, 102538714, 275597098, 742674804, 2006661720, 5436008057, 14763754746, 40196603110, 109703958381, 300091975184, 822705857129 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Caterpillar

MAPLE

with(numtheory):

b:= proc(n) option remember; `if`(n<=1, n,

      (add(add(d*b(d), d=divisors(j))*b(n-j), j=1..n-1))/(n-1))

    end:

a:= n-> b(n) -(add(b(k) *b(n-k), k=0..n)-`if`(irem(n, 2)=0,

        b(n/2), 0))/2 -ceil(2^(n-4) + 2^(iquo(n-2, 2)-1)):

seq(a(n), n=1..40); # Alois P. Heinz, May 18 2013

MATHEMATICA

b[n_] := b[n] = If[n <= 1, n, (Sum[Sum[d*b[d], {d, Divisors[j]}]*b[n - j], {j, 1, n-1}])/(n-1)]; a[n_] := b[n] - (Sum[b[k]*b[n-k], {k, 0, n}] - If[ Mod[n, 2] == 0, b[n/2], 0])/2 - Ceiling[2^(n-4) + 2^(Quotient[n-2, 2] - 1)]; Table[a[n], {n, 1, 40}] (* Jean-Fran├žois Alcover, Feb 19 2016, after Alois P. Heinz *)

CROSSREFS

Cf. A000055, A005418.

Sequence in context: A247103 A036542 A084266 * A037496 A180762 A134326

Adjacent sequences:  A052468 A052469 A052470 * A052472 A052473 A052474

KEYWORD

nonn

AUTHOR

Eric W. Weisstein

EXTENSIONS

a(14) and up from Eric W. Weisstein, Jul 17 2004.

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 19 03:11 EDT 2019. Contains 322237 sequences. (Running on oeis4.)