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 A257243 Tree R defined as the subtree of A257242 tree made of all shortest walks. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A000045, A257242. Sequence in context: A180165 A142249 A274705 * A097351 A207330 A048600 Adjacent sequences:  A257240 A257241 A257242 * A257244 A257245 A257246 KEYWORD nonn,tabf AUTHOR Michel Marcus, Apr 19 2015 STATUS approved

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Last modified November 27 02:53 EST 2021. Contains 349344 sequences. (Running on oeis4.)
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