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A295783
First differences of A294443.
2
0, 1, 1, 2, 2, 6, 7, 11, 17, 30, 40, 73, 109, 165, 269, 441, 675, 1076, 1671, 2699, 4256, 6726, 10585, 16969, 26524, 42386, 66979
OFFSET
1,4
COMMENTS
a(n) is the number of distinct numerators that exist in row n of the Kepler tree A294442 but not yet in row n-1 of the tree (assuming a row count such that 1/1 is in row 0).
It is the number of numerators that are "new" in row n (because the set of denominators of row n-1 contributes to the set of numerators of row n).
a(n) is nonnegative because A294443 is monotonically increasing (because all numerators of one row become numerators of the next row).
Define the "entry level" E(j) as the smallest row number at which denominator j appears in A294442 (again: row counts start at 1/1 as row 0), then a(n+1) is the number of occurrences of n in j: a(n+1) = #{j: E(j)=n}.
It is likely that E(j) = A178047(j), verified for the first 10000 terms.
MATHEMATICA
Differences@ Map[Length@ Union@ Numerator@ # &, #] &@ Nest[Append[#, Flatten@ Map[{#1/(#1 + #2), #2/(#1 + #2)} & @@ {Numerator@ #, Denominator@ #} &, Last@ #]] &, {{1/1}, {1/2}}, 21] (* Michael De Vlieger, Apr 18 2018 *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
R. J. Mathar, Nov 27 2017
EXTENSIONS
a(25)-a(27) from Michael De Vlieger, Apr 18 2018
STATUS
approved