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A241389
Number of partitions p of n such that the number of distinct parts is a part and max(p) - min(p) is not a part.
5
0, 1, 1, 1, 1, 2, 1, 3, 3, 5, 6, 10, 13, 17, 25, 34, 46, 61, 80, 108, 141, 182, 236, 307, 376, 499, 618, 783, 970, 1233, 1491, 1884, 2306, 2841, 3452, 4277, 5128, 6299, 7574, 9176, 11046, 13333, 15882, 19114, 22803, 27154, 32308, 38435, 45476, 53904, 63628
OFFSET
0,6
FORMULA
a(n) + A241387(n) + A241388(n) = A241391(n) for n >= 0.
EXAMPLE
a(9) counts these 5 partitions: 72, 531, 522, 3222, 111111111.
MATHEMATICA
z = 40; f[n_] := f[n] = IntegerPartitions[n]; d[p_] := d[p] = Length[DeleteDuplicates[p]];
Table[Count[f[n], p_ /; MemberQ[p, d[p]] && MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241387 *)
Table[Count[f[n], p_ /; ! MemberQ[p, d[p]] && MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241388 *)
Table[Count[f[n], p_ /; MemberQ[p, d[p]] && ! MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241389 *)
Table[Count[f[n], p_ /; ! MemberQ[p, d[p]] && ! MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241390 *)
Table[Count[f[n], p_ /; MemberQ[p, d[p]] || MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241391 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 21 2014
STATUS
approved