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A212187
Number of distinct sums of reciprocals of parts of partitions of n.
1
1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 41, 55, 75, 97, 129, 166, 213, 272, 343, 430, 536, 664, 822, 1008, 1230, 1495, 1808, 2178, 2616, 3122, 3720, 4416, 5221, 6164, 7249, 8497, 9941, 11593, 13481, 15665, 18150, 20971, 24184, 27827, 31974, 36650, 41944, 47930, 54670
OFFSET
0,3
COMMENTS
This is also the number of distinct spring constants you can make with n Belleville washers.
LINKS
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
Sequence in context: A325857 A023030 A246580 * A332280 A035998 A137792
KEYWORD
nonn
AUTHOR
Sachi Hashimoto, Feb 13 2013
EXTENSIONS
a(31)-a(48) from Giovanni Resta, Feb 18 2013
STATUS
approved