OFFSET
0,3
COMMENTS
This is also the number of distinct spring constants you can make with n Belleville washers.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..73
Wikipedia, Belleville washer
EXAMPLE
For n = 4, the partitions are [4], which gives 1/4, [3,1] which gives 1/3+1/1 = 4/3, [2,2] which gives 1/2+1/2 = 1, [2,1,1] which gives 1/2+1/1+1/1 = 5/2 and [1,1,1,1] which gives 1/1+1/1+1/1+1/1 = 4. These five sums are all distinct, so a(4) = 5.
MAPLE
b:= proc(n, i) option remember; `if`(n=0, {0}, `if`(i<1, {},
{b(n, i-1)[], `if`(i>n, {}, map(x-> x+1/i, b(n-i, i)))[]}))
end:
a:= n-> nops(b(n, n)):
seq(a(n), n=0..40); # Alois P. Heinz, Feb 18 2013
MATHEMATICA
a[n_] := Length@Union[Plus @@@ (1/IntegerPartitions[n])]; a/@Range[30] (* Giovanni Resta, Feb 14 2013 *)
b[n_, i_] := b[n, i] = If[n == 0, {0}, If[i < 1, {}, Union @ Flatten @ {b[n, i-1], If[i > n, {}, Map[Function[x, x + 1/i], b[n-i, i]]]}]];
a[n_] := Length[b[n, n]];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, May 28 2018, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Sachi Hashimoto, Feb 13 2013
EXTENSIONS
a(31)-a(48) from Giovanni Resta, Feb 18 2013
STATUS
approved