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A239510 Number of partitions p of n such that if h = min(p), then h is an (h,0)-separator of p; see Comments. 4
0, 0, 0, 0, 1, 1, 2, 4, 5, 7, 11, 13, 18, 24, 30, 37, 48, 59, 73, 90, 109, 132, 163, 193, 233, 280, 334, 397, 475, 559, 663, 784, 924, 1085, 1279, 1494, 1751, 2049, 2392, 2784, 3248, 3769, 4382, 5081, 5887, 6808, 7879, 9087, 10486, 12083, 13910, 15988, 18384 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

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..53.

EXAMPLE

a(9) counts these 5 partitions: 612, 513, 414, 423, 312121.

MATHEMATICA

z = 75; Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, Min[p]] == Length[p] - 1], {n, 1, z}]  (* A239510 *)

Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, 2 Min[p]] == Length[p] - 1], {n, 1, z}]  (* A239511 *)

Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, Max[p]] == Length[p] - 1], {n, 1, z}]  (* A237828 *)

Table[Count[Rest[IntegerPartitions[n]], p_ /; 2 Count[p, Length[p]] == Length[p] - 1], {n, 1, z}]  (* A239513 *)

Table[Count[Rest[IntegerPartitions[n]], p_ /; 2 Count[p, Max[p] - Min[p]] == Length[p] - 1], {n, 1, z}] (* A239514 *)

CROSSREFS

Cf. A239511, A237828, A239513, A239514, A239482.

Sequence in context: A192590 A028289 A307872 * A039673 A097581 A090614

Adjacent sequences:  A239507 A239508 A239509 * A239511 A239512 A239513

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 24 2014

STATUS

approved

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Last modified October 1 02:38 EDT 2022. Contains 357134 sequences. (Running on oeis4.)