login
A241384
Number of partitions p of n such that the number of parts is a part and max(p) - min(p) is not a part.
5
0, 1, 0, 0, 1, 2, 0, 4, 3, 5, 5, 9, 8, 17, 14, 26, 29, 43, 46, 71, 76, 109, 120, 162, 185, 251, 285, 375, 440, 560, 653, 831, 967, 1209, 1417, 1743, 2045, 2505, 2925, 3553, 4166, 5014, 5864, 7040, 8213, 9798, 11431, 13555, 15795, 18671, 21693, 25536, 29651
OFFSET
0,6
FORMULA
a(n) + A241382(n) + A241383(n) = A241386(n) for n >= 0.
EXAMPLE
a(9) counts these 5 partitions: 72, 531, 51111, 4221, 333.
MATHEMATICA
z = 40; f[n_] := f[n] = IntegerPartitions[n];
Table[Count[f[n], p_ /; MemberQ[p, Length[p]] && MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241382 *)
Table[Count[f[n], p_ /; ! MemberQ[p, Length[p]] && MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241383 *)
Table[Count[f[n], p_ /; MemberQ[p, Length[p]] && ! MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241384 *)
Table[Count[f[n], p_ /; ! MemberQ[p, Length[p]] && ! MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241385 *)
Table[Count[f[n], p_ /; MemberQ[p, Length[p]] || MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A241386 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 21 2014
STATUS
approved