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A239953
Number of partitions of n such that twice the least part is the number of distinct parts.
1
0, 0, 0, 1, 2, 4, 5, 8, 9, 12, 14, 17, 18, 23, 25, 28, 33, 39, 44, 54, 61, 77, 92, 112, 131, 167, 194, 246, 280, 352, 401, 501, 562, 697, 779, 939, 1055, 1274, 1401, 1684, 1846, 2186, 2408, 2825, 3103, 3617, 3969, 4583, 5045, 5801, 6367, 7304, 8050, 9150
OFFSET
0,5
LINKS
EXAMPLE
a(6) counts these 5 partitions : 51, 42, 3111, 22111, 21111.
MAPLE
b:= proc(n, i, d) option remember; `if`(2*min(i, n)<d+1, 0,
`if`(irem(n, i)=0 and 2*i=d+1, 1, b(n, i-1, d)+
add(b(n-i*j, i-1, d+1), j=1..n/i)))
end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..60); # Alois P. Heinz, Apr 02 2014
MATHEMATICA
z = 60; d[p_] := d[p] = Length[DeleteDuplicates[p]]; Table[Count[ IntegerPartitions[n], p_ /; d[p] == 2 Min[p]], {n, 0, z}] (* A239953 *)
(* Second program: *)
b[n_, i_, d_] := b[n, i, d] = If[2*Min[i, n] < d + 1, 0,
If[Mod[n, i] == 0 && 2*i == d + 1, 1, b[n, i - 1, d] +
Sum[b[n - i*j, i - 1, d + 1], {j, 1, n/i}]]];
a[n_] := b[n, n, 0];
a /@ Range[0, 60] (* Jean-François Alcover, May 31 2021, after Alois P. Heinz *)
CROSSREFS
Cf. A239948.
Sequence in context: A348458 A339816 A002541 * A321324 A343013 A259558
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 30 2014
STATUS
approved