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 A000550 Number of trees of diameter 7. (Formerly M2969 N1201) 3
 1, 3, 14, 42, 128, 334, 850, 2010, 4625, 10201, 21990, 46108, 94912, 191562, 380933, 746338, 1444676, 2763931, 5235309, 9822686, 18275648, 33734658, 61826344, 112550305, 203627610, 366267931, 655261559, 1166312530, 2066048261, 3643352362, 6397485909, 11188129665, 19491131627, 33831897511, 58519577756, 100885389220, 173368983090, 297021470421, 507378371670, 864277569606, 1468245046383, 2487774321958, 4204663810414, 7089200255686, 11924621337321, 20012746962064, 33513139512868, 56001473574091, 93387290773141, 155419866337746 (list; graph; refs; listen; history; text; internal format)
 OFFSET 8,2 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). 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 = 8..2500 J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478. FORMULA G.f.: a(x)=(r(x)^2+r(x^2))/2, where r(x) is the generating function of A000235. - Sean A. Irvine, Nov 21 2010 MAPLE b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1 or k<1, 0,      add(binomial(b((i-1)\$2, k-1)+j-1, j)*b(n-i*j, i-1, k), j=0..n/i)))     end: g:= n-> b((n-1)\$2, 3) -b((n-1)\$2, 2): a:= n-> (add(g(i)*g(n-i), i=0..n)+`if`(n::even, g(n/2), 0))/2: seq(a(n), n=8..40);  # Alois P. Heinz, Feb 09 2016 MATHEMATICA m = 50; r[x_] = (Rest @ CoefficientList[ Series[ x*Product[ (1 - x^k)^(- PartitionsP[k-1]), {k, 1, m+3}], {x, 0, m+3}], x] - PartitionsP[ Range[0, m+2]]).(x^Range[m+3]); A000550 = CoefficientList[(r[x]^2 + r[x^2])/2, x][[9 ;; m+8]] (* Jean-François Alcover, Feb 09 2016 *) CROSSREFS Cf. A034853, A000306 (diameter 8) Sequence in context: A296267 A104905 A055650 * A124650 A291138 A063903 Adjacent sequences:  A000547 A000548 A000549 * A000551 A000552 A000553 KEYWORD nonn AUTHOR EXTENSIONS More terms from Sean A. Irvine, Nov 21 2010 STATUS approved

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Last modified May 27 13:00 EDT 2020. Contains 334657 sequences. (Running on oeis4.)