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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A253062 Largest order of a rooted tree that does not contain a rooted caterpillar subtree of order n. 1
0, 1, 2, 3, 5, 7, 11, 16, 23, 34, 49, 70, 103, 148, 211, 310, 445, 634, 931, 1336, 1903, 2794, 4009, 5710, 8383, 12028, 17131, 25150, 36085, 51394, 75451, 108256, 154183, 226354, 324769, 462550, 679063, 974308, 1387651, 2037190, 2922925, 4162954, 6111571 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..43.

Stephan Brandt, Janina Müttel, Dieter Rautenbach, The circumference of the square of a connected graph, Combinatorica 34 (2014), no. 5, 547--559. MR3276436.

FORMULA

See Maple code.

Conjectures from Colin Barker, Feb 21 2015: (Start)

a(n) = a(n-1)+3*a(n-3)-3*a(n-4) for n>10.

G.f.: -x^2*(x^8-x^7+x^6-x^5+x^4+x^3-x^2-x-1) / ((x-1)*(3*x^3-1)).

(End)

MAPLE

f:=proc(k, i)

if i=1 then (23*3^k-1)/2

elif i=2 then (33*3^k-1)/2

else (47*3^k-1)/2; fi;

end;

g:=proc(n) local r, s;

s := (n mod 3); if s=0 then s:=s+3; fi; r:=(n-s)/3;

f(r-2, s);

end;

a:=[0, 1, 2, 3, 5, 7, 11, 16, 23];

for n from 10 to 50 do a:=[op(a), g(n)]; od;

CROSSREFS

Cf. A253063.

Sequence in context: A118084 A232481 A232482 * A117590 A226541 A281578

Adjacent sequences:  A253059 A253060 A253061 * A253063 A253064 A253065

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 21 2015

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 May 23 11:20 EDT 2019. Contains 323514 sequences. (Running on oeis4.)