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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Stephan Brandt, Janina MÃ¼ttel, 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 Adjacent sequences:  A253059 A253060 A253061 * A253063 A253064 A253065 KEYWORD nonn AUTHOR N. J. A. Sloane, Jan 21 2015 STATUS approved

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Last modified May 26 14:52 EDT 2020. Contains 334626 sequences. (Running on oeis4.)