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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
OFFSET
1,3
LINKS
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: A232481 A232482 A332062 * A117590 A308991 A326467
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 21 2015
STATUS
approved