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 A001137 Number of black-rooted red-black trees with n internal nodes. 2
 1, 2, 2, 4, 8, 16, 33, 56, 90, 164, 330, 688, 1440, 3008, 6291, 13168, 27604, 57896, 120730, 248312, 501464, 995664, 1954582, 3821328, 7495996, 14848472, 29815976, 60741680, 125363472, 261452256, 549461078, 1160693056, 2459679936, 5221717888 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..900 F. Ruskey, Information on Red-Black Trees Eric Weisstein's World of Mathematics, Red-Black Tree. Index entries for sequences related to rooted trees FORMULA G.f. satisfies: A(x) = x*(1+x)^2*(1 + A((x+x^2)^2)). - Paul D. Hanna, Jun 14 2012 MATHEMATICA m = 35; A[_] = 0; Do[A[x_] = x*(1 + x)^2*(1 + A[(x + x^2)^2]) + O[x]^m // Normal, {m}]; CoefficientList[A[x]/x, x] (* Jean-François Alcover, Oct 19 2019 *) PROG (PARI) {a(n)=local(A=x); for(i=1, n, A=x*(1+x)^2*(1 + subst(A, x, (x+x^2)^2+x*O(x^n)))); polcoeff(A, n)} \\ Paul D. Hanna, Jun 14 2012 CROSSREFS Cf. A001131. Sequence in context: A318187 A217931 A090129 * A123593 A122748 A108774 Adjacent sequences: A001134 A001135 A001136 * A001138 A001139 A001140 KEYWORD nonn AUTHOR Frank Ruskey EXTENSIONS More terms from Sean A. Irvine, Mar 08 2012 STATUS approved

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Last modified August 11 21:40 EDT 2024. Contains 375073 sequences. (Running on oeis4.)