OFFSET
0,2
COMMENTS
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
KEYWORD
nonn,look
AUTHOR
Paul D. Hanna, Nov 19 2006
STATUS
approved