cp's OEIS Frontend

A294444 Number of distinct numbers appearing as denominators in row n of Kepler's triangle A294442.

%I A294444 #13 Dec 06 2024 11:11:07
%S A294444 1,1,1,2,3,6,10,16,29,51,83,148,246,402,650,1084,1740,2803,4458
%N A294444 Number of distinct numbers appearing as denominators in row n of Kepler's triangle A294442.
%C A294444 It would be nice to have a formula or recurrence.
%e A294444 Row 4 of A294442 contains eight fractions, 1/5, 4/5, 3/7, 4/7, 2/7, 2/7, 3/8, 5/8.
%e A294444 There are three distinct denominators, so a(4) = 3.
%p A294444 # S[n] is the list of fractions, written as pairs [i, j], in row n of Kepler's triangle; nc is the number of distinct numerators, and dc the number of distinct denominators
%p A294444 S[0]:=[[1,1]]; S[1]:=[[1,2]];
%p A294444 nc:=[1,1]; dc:=[1,1];
%p A294444 for n from 2 to 18 do
%p A294444 S[n]:=[];
%p A294444 for k from 1 to nops(S[n-1]) do
%p A294444 t1:=S[n-1][k];
%p A294444 a:=[t1[1],t1[1]+t1[2]];
%p A294444 b:=[t1[2],t1[1]+t1[2]];
%p A294444 S[n]:=[op(S[n]),a,b];
%p A294444 od:
%p A294444 listn:={};
%p A294444 for k from 1 to nops(S[n]) do listn:={op(listn), S[n][k][1]}; od:
%p A294444 c:=nops(listn);  nc:=[op(nc),c];
%p A294444 listd:={};
%p A294444 for k from 1 to nops(S[n]) do listd:={op(listd), S[n][k][2]}; od:
%p A294444 c:=nops(listd);  dc:=[op(dc),c];
%p A294444 od:
%p A294444 nc; # A293160
%p A294444 dc; # this sequence
%Y A294444 Cf. A294442.
%Y A294444 See A293160 for the number of distinct numerators, or for numerators or denominators in the Stern-Brocot triangle A002487.
%K A294444 nonn,more
%O A294444 0,4
%A A294444 _N. J. A. Sloane_, Nov 20 2017