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

1, 1, 1, 2, 3, 6, 10, 16, 29, 51, 83, 148, 246, 402, 650, 1084, 1740, 2803, 4458

Offset: 0

Author

N. J. A. Sloane, Nov 20 2017

Keywords

• nonn
• more

Comments

It would be nice to have a formula or recurrence.

Examples

			Row 4 of A294442 contains eight fractions, 1/5, 4/5, 3/7, 4/7, 2/7, 2/7, 3/8, 5/8.
There are three distinct denominators, so a(4) = 3.
		

Crossrefs

Cf. A294442.

See A293160 for the number of distinct numerators, or for numerators or denominators in the Stern-Brocot triangle A002487.

Programs

Maple

# 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
S[0]:=[[1,1]]; S[1]:=[[1,2]];
nc:=[1,1]; dc:=[1,1];
for n from 2 to 18 do
S[n]:=[];
for k from 1 to nops(S[n-1]) do
t1:=S[n-1][k];
a:=[t1[1],t1[1]+t1[2]];
b:=[t1[2],t1[1]+t1[2]];
S[n]:=[op(S[n]),a,b];
od:
listn:={};
for k from 1 to nops(S[n]) do listn:={op(listn), S[n][k][1]}; od:
c:=nops(listn);  nc:=[op(nc),c];
listd:={};
for k from 1 to nops(S[n]) do listd:={op(listd), S[n][k][2]}; od:
c:=nops(listd);  dc:=[op(dc),c];
od:
nc; # A293160
dc; # this sequence