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A237828 Number of partitions of n such that 2*(least part) + 1 = greatest part. 9
0, 0, 0, 1, 1, 2, 4, 4, 6, 9, 10, 12, 17, 18, 22, 27, 31, 34, 42, 45, 53, 61, 66, 72, 86, 92, 103, 113, 125, 135, 154, 163, 180, 197, 213, 229, 257, 271, 294, 318, 346, 368, 404, 426, 463, 497, 532, 564, 616, 651, 700, 747, 798, 844, 912, 962, 1033, 1097 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Also, the number of partitions p of n such that if h = max(p), then h is an (h,0)-separator of p; for example, a(10) counts these 9 partitions: 181, 271, 361, 262, 451, 352, 343, 23131, 1212121. - Clark Kimberling, Mar 24 2014

LINKS

Table of n, a(n) for n=1..58.

EXAMPLE

a(8) = 4 counts these partitions: 3311, 3221, 32111, 311111.

MATHEMATICA

z = 64; q[n_] := q[n] = IntegerPartitions[n];

Table[Count[q[n], p_ /; 3 Min[p] = = Max[p]], {n, z}] (* A237825*)

Table[Count[q[n], p_ /; 4 Min[p] = = Max[p]], {n, z}] (* A237826 *)

Table[Count[q[n], p_ /; 5 Min[p] = = Max[p]], {n, z}] (* A237827 *)

Table[Count[q[n], p_ /; 2 Min[p] + 1 = = Max[p]], {n, z}] (* A237828 *)

Table[Count[q[n], p_ /; 2 Min[p] - 1 = = Max[p]], {n, z}] (* A237829 *)

Table[Count[IntegerPartitions[n], _?(2*Min[#]+1==Max[#]&)], {n, 60}] (* Harvey P. Dale, Jun 25 2017 *)

CROSSREFS

Cf. A237757, A237825-A237827, A237829, A000041.

Sequence in context: A292671 A210948 A008133 * A340626 A351489 A022471

Adjacent sequences: A237825 A237826 A237827 * A237829 A237830 A237831

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Feb 16 2014

STATUS

approved

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Last modified December 9 23:05 EST 2022. Contains 358710 sequences. (Running on oeis4.)