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A240184 Number of partitions of n such that (greatest part) > (multiplicity of least part). 3
0, 0, 1, 2, 2, 5, 6, 11, 14, 20, 29, 41, 52, 76, 98, 130, 170, 227, 288, 378, 477, 615, 778, 985, 1228, 1551, 1928, 2399, 2964, 3670, 4498, 5538, 6755, 8251, 10027, 12175, 14715, 17802, 21420, 25764, 30886, 37009, 44181, 52731, 62730, 74570, 88435, 104762 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
A240178(n) + A240183(n) + a(n ) = A000041(n) for n >= 1.
EXAMPLE
a(6) counts these 6 partitions: 6, 51, 42, 411, 33, 321.
MATHEMATICA
z = 60; f[n_] := f[n] = IntegerPartitions[n];
t1 = Table[Count[f[n], p_ /; Max[p] < Count[p, Min[p]]], {n, 0, z}] (* A240178 *)
t2 = Table[Count[f[n], p_ /; Max[p] <= Count[p, Min[p]]], {n, 0, z}] (* A240182 *)
t3 = Table[Count[f[n], p_ /; Max[p] == Count[p, Min[p]]], {n, 0, z}] (* A240183 *)
t4 = Table[Count[f[n], p_ /; Max[p] > Count[p, Min[p]]], {n, 0, z}] (* A240184 *)
t5 = Table[Count[f[n], p_ /; Max[p] >= Count[p, Min[p]]], {n, 0, z}] (* A240179 *)
CROSSREFS
Sequence in context: A348324 A007988 A241449 * A317853 A238517 A335240
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 02 2014
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)