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A257243
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Tree R defined as the subtree of A257242 tree made of all shortest walks.
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1
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1, 1, 2, 1, 3, 3, 1, 5, 2, 4, 4, 2, 8, 5, 1, 7, 3, 5, 7, 3, 13, 3, 7, 5, 3, 11, 7, 1, 9, 5, 9, 11, 5, 21, 8, 2, 12, 4, 6, 10, 4, 18, 4, 10, 6, 4, 14, 12, 2, 16, 8, 14, 18, 8, 34, 5, 11, 9, 5, 19, 9, 1, 11, 7, 13, 15, 7, 29, 11, 3, 17, 5, 7, 13, 5, 23, 7, 17
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OFFSET
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1,3
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COMMENTS
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"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).
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LINKS
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EXAMPLE
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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
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1
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2--------------
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1 3---------
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3----- 1 5-----
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2 4---- 4---- 2 8----
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5 1 7 3 5 7 3 13
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PROG
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(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); ); }
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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