

A239484


Number of (4,0)separable partitions of n; see Comments.


4



0, 1, 1, 2, 1, 2, 3, 4, 5, 6, 7, 9, 11, 13, 15, 19, 22, 26, 31, 36, 42, 51, 58, 68, 79, 92, 107, 125, 143, 165, 191, 221, 253, 293, 333, 383, 440, 503, 574, 657, 747, 853, 971, 1105, 1253, 1427, 1616, 1833, 2076, 2349, 2655, 3006, 3389, 3826, 4313, 4861
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

5,4


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 hseparable if it is (h,i)separable for i = 0,1,2.


LINKS

Table of n, a(n) for n=5..60.


EXAMPLE

The (4,0)separable partitions of 12 are 741, 642, 543, 24141, so that a(12) = 4.


MATHEMATICA

z = 65; 1 + Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, 1] == Length[p]  1], {n, 2, z}] (* A165652 *)
1 + Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, 2] == Length[p]  1], {n, 3, z}] (* A239482 *)
1 + Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, 3] == Length[p]  1], {n, 4, z}] (* A239483 *)
1 + Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, 4] == Length[p]  1], {n, 5, z}] (* A239484 *)
1 + Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, 5] == Length[p]  1], {n, 6, z}] (* A239485 *)


CROSSREFS

Cf. A239467, A165652, A239482, A239483, A239485.
Sequence in context: A220661 A137846 A080915 * A058714 A057045 A237753
Adjacent sequences: A239481 A239482 A239483 * A239485 A239486 A239487


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Mar 20 2014


STATUS

approved



