OFFSET
1,4
COMMENTS
"By the random Fibonacci tree of the pair (a,b) we mean the binary tree denoted by T(a,b) and defined in the following way: a is the root, b its only child; if x is the parent of y, then y has two children, which are x + y and abs(x-y)."
"The sequence of labels in the tree read in breadth-first order (1, 1, 0, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 5. . . ), gives an example of a 2-regular sequence in the terminology given by Allouche and Shallit (see links)."
LINKS
J.-P. Allouche and J. Shallit, The ring of k-regular sequences, Theoretical Computer Sci., 98 (1992), 163-197.
J.-P. Allouche and J. Shallit, The ring of k-regular sequences, II, Theoret. Computer Sci., 307 (2003), 3-29.
B. Rittaud, On the Average Growth of Random Fibonacci Sequences, Journal of Integer Sequences, 10 (2007), Article 07.2.4.
EXAMPLE
[1];
[1];
[0, 2];
[1, 1, 1, 3];
[1, 1, 1, 1, 1, 3, 1, 5];
[0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 4, 2, 4, 2, 8];
...
PROG
(PARI) lchild(a, b) = abs(b-a);
rchild(a, b) = b+a;
tablf(nn) = {print(prow = [1]); print(crow = [1]); nrow = vector(2); nrow[1] = lchild(prow[1], crow[1]); nrow[2] = rchild(prow[1], prow[1]); print(nrow); for (n=4, nn, prow = crow; crow = nrow; nrow = vector(4*#prow); inew = 0; ichild = 0; for (inode=1, #prow, node = prow[inode]; child = crow[ichild++]; nrow[inew++] = lchild(node, child); nrow[inew++] = rchild(node, child); child = crow[ichild++]; nrow[inew++] = lchild(node, child); nrow[inew++] = rchild(node, child); ); print(nrow); ); }
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Michel Marcus, Apr 19 2015
STATUS
approved