A115855 Number of partitions of 1 into fractions i/j with 1<=i

0, 1, 3, 6, 12, 21, 35, 58, 106, 188, 243, 493, 593, 1062, 3275, 5507, 5803, 12426, 12915, 42410, 131772, 167587, 168841, 428012, 839367, 1015501, 1968161, 5787286, 5791850, 15163758, 15170599, 28838712, 75983559, 82753547, 486356262, 1158442726, 1158464362

Offset: 1

Author

Reinhard Zumkeller, Feb 01 2006

Keywords

• nonn

Examples

			a(4) = #{1/2+1/2, 1/2+1/4+1/4, 1/3+2/3, 1/3+1/3+1/3, 1/4+3/4, 1/4+1/4+1/4+1/4} = 6.
		

Crossrefs

Cf. A000041, A002966, A038566, A038567, A115856, A116084.

Programs

Mathematica

Table[Length@ Select[Flatten[Map[IntegerPartitions[1, {#}, Rest@ Union[Flatten@ TensorProduct[#, 1/#] &@ Range@ n /. {Integer -> 0, k /; k > 1 -> 0}]] &, Range@ n], 1], Total@ # == 1 &], {n, 25}] (* Michael De Vlieger, Jul 15 2016 *) (* or *)
a[n_] := Sum[ Length@ IntegerPartitions[1, {k}, Union@ Flatten[ Table[i/j, {j, n}, {i, j-1}]]], {k, n}]; Array[a, 20] (* Giovanni Resta, Jun 15 2017 *)

Formula

A115856(n) = a(n+1) - a(n).

Extensions

a(21)-a(28) from Michael De Vlieger, Jul 15 2016

More terms from Jinyuan Wang, Dec 11 2024