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 A125051 The sub-Fibonacci tree; a rooted tree in which every node with label k and parent node with label g has g child nodes that are assigned labels beginning with k+1 through k+g; the tree starts at generation n=0 with a root node labeled '1' and a child node labeled '2'. 3
 1, 2, 3, 4, 5, 5, 6, 7, 6, 7, 8, 6, 7, 8, 9, 7, 8, 9, 10, 8, 9, 10, 11, 7, 8, 9, 10, 11, 8, 9, 10, 11, 12, 9, 10, 11, 12, 13, 7, 8, 9, 10, 11, 8, 9, 10, 11, 12, 9, 10, 11, 12, 13, 10, 11, 12, 13, 14, 8, 9, 10, 11, 12, 13, 9, 10, 11, 12, 13, 14, 10, 11, 12, 13, 14, 15, 11, 12, 13, 14, 15, 16, 9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The maximum label for nodes in generation n is Fibonacci(n+2) for n>=0. The total number of nodes in generation n equals A005270(n+2) for n>=0. The sum of the labels for nodes in generation n equals A125052(n). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..24903 (generations 0..8) Peter C. Fishburn and Fred S. Roberts, Elementary sequences, sub-Fibonacci sequences, Discrete Appl. Math. 44 (1993), no. 1-3, 261-281. EXAMPLE The initial nodes of the tree for generations 0..5 are: gen.0: [1]; gen.1: [2]; gen.2: [3]; gen.3: [4,5]; gen.4: (4)->[5,6,7],(5)->[6,7,8]; gen.5: (5)->[6,7,8,9],(6)->[7,8,9,10],(7)->[8,9,10,11], (6)->[7,8,9,10,11],(7)->[8,9,10,11,12],(8)->[9,10,11,12,13]. By definition, there are 2 child nodes for node [3] of gen.2 since the parent of node [3] has label 2; likewise, there are 3 child nodes for nodes [4] and [5] of gen.3 since the parent of both nodes has label 3. The number of nodes in generation n begins: 1, 1, 1, 2, 6, 27, 177, 1680, 23009, 455368, 13067353, ... The sum of the labels for nodes in generation n begins: 1, 2, 3, 9, 39, 252, 2361, 32077, 631058, 18035534, ... MAPLE g:= proc(n) option remember; `if`(n=0, [[1, 1]], map(x-> seq([x[2], x[2]+i], i=1..x[1]), g(n-1))) end: T:= n-> map(x-> x[2], g(n)): a:= proc() local i, l; i, l:= -1, []; proc(n) while nops(l)<=n do i:=i+1; l:=[l[], T(i)[]] od; l[n+1] end end(): seq(a(n), n=0..200); # Alois P. Heinz, Feb 08 2013 CROSSREFS Cf. A005270, A125052. Sequence in context: A097873 A005375 A138370 * A064067 A202306 A275579 Adjacent sequences: A125048 A125049 A125050 * A125052 A125053 A125054 KEYWORD nonn,look AUTHOR Paul D. Hanna, Nov 19 2006 STATUS approved

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Last modified December 7 05:41 EST 2022. Contains 358649 sequences. (Running on oeis4.)