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 A245151 Number T(n,k) of n-node unlabeled rooted trees with thickening limbs and root outdegree (branching factor) k; triangle T(n,k), n>=1, 0<=k<=n-1, read by rows. 12
 1, 0, 1, 0, 1, 1, 0, 2, 0, 1, 0, 3, 1, 0, 1, 0, 5, 1, 0, 0, 1, 0, 7, 3, 1, 0, 0, 1, 0, 12, 3, 1, 0, 0, 0, 1, 0, 17, 8, 1, 1, 0, 0, 0, 1, 0, 28, 9, 3, 1, 0, 0, 0, 0, 1, 0, 42, 21, 3, 1, 1, 0, 0, 0, 0, 1, 0, 69, 28, 5, 1, 1, 0, 0, 0, 0, 0, 1, 0, 105, 56, 9, 3, 1, 1, 0, 0, 0, 0, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS In a rooted tree with thickening limbs the outdegree of a parent node is smaller than or equal to the outdegree of any of its non-leaf child nodes. T(n+1,1) = Sum_{k=0..n-1} T(n,k) for n>=1. T(n+1,n) = T(2n+1,n) = 1 for n>=0. T(n,1+floor((n-1)/2)) = 0 for n>3. LINKS Alois P. Heinz, Rows n = 1..141, flattened EXAMPLE The A245152(5) = 5 5-node rooted trees with thickening limbs sorted by root outdegree are: : o   o     o   :     o   :    o    : : |   |     |   :    / \  :  /( )\  : : o   o     o   :   o   o : o o o o : : |   |    /|\  :  / \    :         : : o   o   o o o : o   o   :         : : |  / \        :         :         : : o o   o       :         :         : : |             :         :         : : o             :         :         : :               :         :         : : ------1------ : ---2--- : ---4--- : Thus row 5 = [0, 3, 1, 0, 1]. Triangle T(n,k) begins: 1; 0,   1; 0,   1,  1; 0,   2,  0,  1; 0,   3,  1,  0, 1; 0,   5,  1,  0, 0, 1; 0,   7,  3,  1, 0, 0, 1; 0,  12,  3,  1, 0, 0, 0, 1; 0,  17,  8,  1, 1, 0, 0, 0, 1; 0,  28,  9,  3, 1, 0, 0, 0, 0, 1; 0,  42, 21,  3, 1, 1, 0, 0, 0, 0, 1; 0,  69, 28,  5, 1, 1, 0, 0, 0, 0, 0, 1; 0, 105, 56,  9, 3, 1, 1, 0, 0, 0, 0, 0, 1; 0, 176, 81, 12, 3, 1, 1, 0, 0, 0, 0, 0, 0, 1; MAPLE b:= proc(n, i, h, v) option remember; `if`(n=0,       `if`(v=0, 1, 0), `if`(i<1 or v<1 or n b(n-1\$2, k\$2): seq(seq(T(n, k), k=0..n-1), n=1..20); MATHEMATICA b[n_, i_, h_, v_] := b[n, i, h, v] = If[n == 0, If[v == 0, 1, 0], If[i<1 || v<1 || n

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)