The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A002989 Number of n-node trees with a forbidden limb of length 3. (Formerly M1082) 2
 1, 1, 1, 1, 1, 2, 4, 7, 14, 28, 61, 131, 297, 678, 1592, 3770, 9096, 22121, 54451, 135021, 337651, 849698, 2152048, 5479408, 14022947, 36048514, 93061268, 241160180, 627179689, 1636448181, 4282964600, 11241488853, 29584389474 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS A tree with a forbidden limb of length k is a tree where the path from any leaf inward hits a branching node or another leaf within k steps. REFERENCES A. J. Schwenk, Almost all trees are cospectral, pp. 275-307 of F. Harary, editor, New Directions in the Theory of Graphs. Academic Press, NY, 1973. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 A. J. Schwenk, Letter to N. J. A. Sloane, Aug 1972 FORMULA G.f.: 1+B(x)+(B(x^2)-B(x)^2)/2 where B(x) is g.f. of A052321. a(n) ~ c * d^n / n^(5/2), where d = 2.851157026715821487965080545784..., c = 0.463162985533004672966744142107... . - Vaclav Kotesovec, Aug 24 2014 MAPLE with(numtheory): g:= proc(n) g(n):= `if`(n=0, 1, add(add(d*(g(d-1)-       `if`(d=3, 1, 0)), d=divisors(j))*g(n-j), j=1..n)/n)     end: a:= n-> `if`(n=0, 1, g(n-1)+(`if`(irem(n, 2, 'r')=0,          g(r-1), 0)-add(g(i-1)*g(n-i-1), i=1..n-1))/2): seq(a(n), n=0..40);  # Alois P. Heinz, Jul 06 2014 MATHEMATICA g[n_] := g[n] = If[n == 0, 1, Sum[Sum[d*(g[d-1]-If[d == 3, 1, 0]), {d, Divisors[j] }]*g[n-j], {j, 1, n}]/n]; a[n_] := If[n == 0, 1, g[n-1] + (If[Mod[n, 2 ] == 0, g[Quotient[n, 2] - 1], 0] - Sum[g[i-1]*g[n-i-1], {i, 1, n-1}])/2]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Feb 26 2015, after Alois P. Heinz *) CROSSREFS Cf. A002955, A002988-A002992, A052318-A052329. Sequence in context: A119341 A119342 A119268 * A293336 A321401 A000671 Adjacent sequences:  A002986 A002987 A002988 * A002990 A002991 A002992 KEYWORD nonn AUTHOR EXTENSIONS More terms, formula and comments from Christian G. Bower, Dec 15 1999 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.

Last modified September 18 07:39 EDT 2020. Contains 337166 sequences. (Running on oeis4.)