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A239689 Number of partitions p of n such that if h = max(p) - min(p), then h is an (h,2)-separator of p; see Comments. 5
0, 0, 0, 1, 0, 0, 1, 1, 0, 2, 0, 1, 3, 2, 1, 4, 0, 4, 5, 5, 4, 5, 5, 7, 7, 10, 6, 15, 10, 13, 13, 14, 16, 20, 18, 26, 24, 29, 28, 34, 27, 39, 40, 47, 46, 57, 55, 65, 63, 75, 72, 83, 85, 101, 101, 117, 115, 136, 134, 157, 156, 170, 181, 200, 197, 229, 230 (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, or 2.

LINKS

Table of n, a(n) for n=1..67.

EXAMPLE

a(13) counts these 3 partitions: 24232, 2321212, 121212121.

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, A239481, A239456, A239499.

Sequence in context: A197119 A124377 A144190 * A177802 A022827 A302764

Adjacent sequences:  A239686 A239687 A239688 * A239690 A239691 A239692

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 25 2014

STATUS

approved

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Last modified September 25 22:56 EDT 2022. Contains 356986 sequences. (Running on oeis4.)