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A264597 Triangle T(n,m) (n >= 2, 0 <= m <= n-1) read by rows, defined in Comments. 3
1, 1, 1, 3, 2, 1, 4, 2, 1, 1, 7, 3, 2, 1, 1, 7, 3, 1, 1, 1, 1, 12, 4, 3, 2, 1, 1, 1, 8, 2, 1, 1, 1, 1, 1, 1, 20, 8, 4, 2, 2, 1, 1, 1, 1, 13, 3, 2, 2, 1, 1, 1, 1, 1, 1, 18, 4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 18, 6, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 31, 8, 6, 4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 20, 6, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 31, 8, 4, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 24, 4, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 39, 10, 6, 4, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

2,4

COMMENTS

We work with 2 X 2 matrices X = [a,b; c,d] with integer entries. Let M be the free monoid generated by L = [1,0; 1,1] and R = [1,1; 0,1]. Let t be the map [a,b; c,d]) -> (a+b)/(c+d). Then T(n,m) is the number of X in M with trace(X)=n and m <= t(X) < m+1.

LINKS

Table of n, a(n) for n=2..154.

M. P. Technau, The Calkin-Wilf Tree and a Trace Condition, Master's Thesis, Julius-Maximilian’s University of Würzburg, Faculty for Mathematics and Computer Science, 2015.

EXAMPLE

Triangle begins:

   1,

   1, 1,

   3, 2, 1,

   4, 2, 1, 1,

   7, 3, 2, 1, 1,

   7, 3, 1, 1, 1, 1,

  12, 4, 3, 2, 1, 1, 1,

   8, 2, 1, 1, 1, 1, 1, 1,

  20, 8, 4, 2, 2, 1, 1, 1, 1,

  13, 3, 2, 2, 1, 1, 1, 1, 1, 1,

  18, 4, 3, 2, 2, 2, 1, 1, 1, 1, 1,

  18, 6, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1,

  31, 8, 6, 4, 3, 2, 2, 1, 1, 1, 1, 1, 1,

  20, 6, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

  ...

CROSSREFS

Row sums are A264598. It appears that the row sums are also twice A257007.

Sequence in context: A194528 A194520 A082727 * A112603 A097294 A060848

Adjacent sequences:  A264594 A264595 A264596 * A264598 A264599 A264600

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Nov 19 2015

STATUS

approved

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Last modified May 15 07:51 EDT 2021. Contains 343909 sequences. (Running on oeis4.)