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A239481 Number of partitions p of n such that if h = 2*min(p), then h is an (h,2)-separator of p; see Comments. 6
0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 1, 2, 3, 4, 5, 7, 6, 9, 13, 13, 17, 22, 25, 32, 39, 43, 55, 67, 78, 93, 113, 132, 158, 191, 217, 260, 308, 357, 424, 498, 576, 676, 792, 916, 1069, 1244, 1436, 1666, 1934, 2225, 2573, 2971, 3410, 3932, 4524, 5183, 5951, 6826 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

COMMENTS

Suppose that p is a partition of n into 2 or more parts and that h is a part of p.  Then p is (h,0)-separable if there is an ordering x, h, x, h, ..., h, x of the parts of p, where each x represents any part of p except h.  Here, the number of h's on the ends of the ordering is 0.  Similarly, p is (h,1)-separable if there is an ordering x, h, x, h, ... , x, h, where the number of h's on the ends is 1; next, p is (h,2)-separable if there is an ordering h, x, h, ... , x, h.  Finally, p is h-separable if it is (h,i)-separable for i = 0,1,2.

LINKS

Table of n, a(n) for n=1..59.

EXAMPLE

a(10) counts these partitions:  424, 23212.

MATHEMATICA

z = 75; Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, Min[p]] == Length[p] + 1], {n, 1, z}]  (* A239729 *)

Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, 2 Min[p]] == Length[p] + 1], {n, 1, z}] (* A239481 *)

Table[Count[Rest[IntegerPartitions[n]], p_ /; 2 Count[p, Max[p]] == Length[p] + 1], {n, 1, z}] (* A239456 *)

Table[Count[Rest[IntegerPartitions[n]], p_ /; 2 Count[p, Length[p]] == Length[p] + 1], {n, 1, z}] (* A239499 *)

Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, Max[p] - Min[p]] == Length[p] + 1], {n, 1, z}]  (*A239689 *)

CROSSREFS

Cf. A239729, A239456, A239499, A239689.

Sequence in context: A230507 A259910 A072549 * A200114 A120652 A330608

Adjacent sequences:  A239478 A239479 A239480 * A239482 A239483 A239484

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 25 2014

STATUS

approved

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Last modified August 12 23:19 EDT 2020. Contains 336440 sequences. (Running on oeis4.)