A119868 Number of different values assumed by a/b+c/d as a,b,c,d range between 1 and n.

1, 6, 21, 44, 124, 158, 382, 558, 899, 1087, 2022, 2328, 3936, 4542, 5463, 6755, 10366, 11306, 16488, 18315, 21092, 23455, 32562, 34901, 43833, 47945, 56749, 61726, 80278, 83515, 106455, 117566, 129575, 139126, 156439, 164489, 203153, 216586, 235914, 249462

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..100

Example

a(2)=6 since we can obtain 6 values, i.e., {1, 3/2, 2, 5/2, 3, 4}.

Maple

fracs:= {1}:
A[1]:= 1:
for n from 2 to 100 do
   fracs:= fracs union {seq(n/i, i=1..n-1)} union {seq(i/n, i=1..n-1)};
   A[n]:= nops({seq(seq(fracs[i]+fracs[j], j=1..i), i=1..nops(fracs))});
od:
seq(A[n], n=1..100); # Robert Israel, Apr 26 2015

Mathematica

Table[Length@Union@Flatten@Table[a/b + c/d, {a, n}, {b, n}, {c, n}, {d, n}], {n, 24}]
Table[Length[Union[#[[1]]/#[[2]]+#[[3]]/#[[4]]&/@Tuples[Range[n], {4}]]], {n, 25}] (* Harvey P. Dale, Mar 04 2013 *)

Crossrefs

Cf. A119867.

Sequence in context: A272684 A180863 A180857 * A175729 A081266 A087863

Adjacent sequences: A119865 A119866 A119867 * A119869 A119870 A119871

Keyword

nonn

Author

Giovanni Resta, May 26 2006

Extensions

More terms from Harvey P. Dale, Mar 04 2013

a(31) to a(40) from Robert Israel, Apr 26 2015

Status

approved