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A241388
Number of partitions p of n such that the number of distinct parts is not a part and max(p) - min(p) is a part.
5
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 5, 2, 7, 10, 15, 14, 30, 28, 49, 56, 81, 89, 135, 148, 212, 246, 327, 377, 506, 578, 759, 883, 1119, 1314, 1651, 1918, 2388, 2789, 3429, 4012, 4880, 5688, 6883, 8029, 9618, 11213, 13388, 15550, 18464, 21431, 25316, 29343
OFFSET
0,13
FORMULA
a(n) + A241387(n) + A241389(n) = A241391(n) for n >= 0.
EXAMPLE
a(9) counts this one partition: 63.
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