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 A052328 Number of rooted trees with a forbidden limb of length 5. 4
 1, 1, 2, 4, 9, 19, 46, 110, 273, 684, 1747, 4505, 11763, 30956, 82153, 219437, 589747, 1593170, 4324445, 11787195, 32251520, 88548011, 243877256, 673605521, 1865445693, 5178574184, 14408195935, 40170674295, 112213616851 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A rooted tree with a forbidden limb of length k is a rooted tree where the path from any leaf inward hits a branching node or the root within k steps. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 N. J. A. Sloane, Transforms FORMULA a(n) satisfies a = SHIFT_RIGHT(EULER(a-b)) where b(5)=1, b(k)=0 if k != 5. a(n) ~ c * d^n / n^(3/2), where d = 2.944791657501974377513779510930324..., c = 0.43624554592719796037836168844839... . - Vaclav Kotesovec, Aug 25 2014 MAPLE with(numtheory): g:= proc(n) g(n):= `if`(n=0, 1, add(add(d*(g(d-1)-       `if`(d=5, 1, 0)), d=divisors(j))*g(n-j), j=1..n)/n)     end: a:= n-> g(n-1): seq(a(n), n=1..35);  # Alois P. Heinz, Jul 04 2014 MATHEMATICA g[n_] := g[n] = If[n==0, 1, Sum[Sum[d(g[d-1] - If[d==5, 1, 0]), {d, Divisors[j]}] g[n-j], {j, 1, n}]/n]; a[n_] := g[n-1]; Array[a, 35] (* Jean-François Alcover, Dec 18 2020, after Alois P. Heinz *) CROSSREFS Cf. A002955, A002988-A002992, A052318-A052329. Column k=5 of A255636. Sequence in context: A134964 A318798 A318851 * A133228 A036717 A000080 Adjacent sequences:  A052325 A052326 A052327 * A052329 A052330 A052331 KEYWORD nonn AUTHOR Christian G. Bower, Dec 15 1999 STATUS approved

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Last modified May 5 22:32 EDT 2021. Contains 343578 sequences. (Running on oeis4.)