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A240858
Number of partitions p of n into distinct parts not including max(p) - min(p).
2
0, 1, 1, 1, 2, 3, 2, 5, 5, 6, 7, 12, 11, 16, 16, 23, 27, 33, 35, 47, 52, 65, 75, 88, 101, 121, 139, 164, 190, 219, 249, 294, 334, 384, 443, 504, 577, 659, 746, 851, 971, 1097, 1242, 1409, 1585, 1790, 2023, 2271, 2557, 2873, 3221, 3612, 4049, 4521, 5054, 5651
OFFSET
0,5
FORMULA
a(n) + A240852(n) = A000009(n) for n >= 0.
EXAMPLE
a(10) counts all 10 partitions of 10 into distinct parts except for 541, 532, 4321, so that a(10) = 7.
MATHEMATICA
z = 40; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &]; Table[Count[f[n], p_ /; MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A240852 *)
Table[Count[f[n], p_ /; !MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A240858 *)
CROSSREFS
Sequence in context: A144307 A144310 A330049 * A035361 A137851 A369742
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 14 2014
STATUS
approved