OFFSET
1,3
COMMENTS
"In other words, we start from 1, with only child 1. Then, the (n-1) first rows being constructed, the n-th one is made of the nodes b such that, denoting by a their parent, the pair (a; b) did not already appear upper in the subtree (that is no row before the n-th one shows the pair(a; b)). The tree R is the restricted subtree of T."
"The sequence of labels in the tree R, read in breadth-first order is a beta-regular sequence, as defined by Allouche, Scheicher and Tichy, where here beta is the numeration system defined by the Fibonacci sequence."
The right diagonal is sequence A000045 (Fibonacci).
LINKS
J.-P. Allouche, K. Scheicher and R. Tichy, Regular maps in generalized number systems, Math. Slovaca 50 (2000), 41-58.
B. Rittaud, On the Average Growth of Random Fibonacci Sequences, Journal of Integer Sequences, 10 (2007), Article 07.2.4.
EXAMPLE
Triangle starts:
1;
1;
2;
1, 3;
3, 1, 5;
2, 4, 4, 2, 8;
5, 1, 7, 3, 5, 7, 3, 13;
...
Tree starts:
1
|
1
|
2--------------
| |
1 3---------
| | |
3----- 1 5-----
| | | | |
2 4---- 4---- 2 8----
| | | | | | | |
5 1 7 3 5 7 3 13
PROG
(PARI) printrow(row) = for (k=1, #row, if (row[k]>0, print1(row[k], ", "))); print();
dchild(a, b) = b-a;
schild(a, b) = b+a;
tablr(nn) = {printrow(prow = [1]); printrow(crow = [1]); nrow = vector(2); nrow[2] = schild(prow[1], crow[1]); printrow(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++]; if (child > 0, nrow[inew++] = dchild(node, child); nrow[inew++] = schild(node, child), nrow[inew++] = -1; nrow[inew++] = -1); child = crow[ichild++]; if (child > 0, nrow[inew++] = dchild(node, child); nrow[inew++] = schild(node, child), nrow[inew++] = -1; nrow[inew++] = -1); ); printrow(nrow); ); }
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Michel Marcus, Apr 19 2015
STATUS
approved