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A241386
Number of partitions p of n such that the number of parts is a part or max(p) - min(p) is a part.
5
0, 1, 0, 1, 2, 4, 4, 8, 10, 15, 19, 24, 35, 45, 57, 76, 98, 123, 161, 198, 252, 313, 388, 472, 597, 722, 891, 1085, 1332, 1602, 1964, 2348, 2852, 3412, 4109, 4889, 5879, 6964, 8317, 9846, 11706, 13795, 16358, 19226, 22695, 26630, 31305, 36621, 42966, 50116
OFFSET
0,5
FORMULA
a(n) + A241385(n) = A000041(n) for n >= 0.
EXAMPLE
a(6) counts these 4 partitions: 42, 321, 2211, 21111.
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