

A239496


Number of (5,1)separable partitions of n; see Comments.


4



0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 2, 2, 3, 3, 3, 3, 5, 5, 7, 8, 9, 10, 13, 14, 17, 20, 23, 26, 32, 35, 42, 48, 55, 63, 75, 83, 97, 111, 127, 144, 168, 188, 217, 246, 280, 317, 365, 409, 467, 528, 598, 674, 768, 861, 977, 1099, 1239, 1392, 1575, 1762, 1987
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,12


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=1..62.


EXAMPLE

The (5,1)separable partitions of 14 are 95, 3515, 2525, so that a(14) = 3.


MATHEMATICA

z = 70; Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, 1] == Length[p]], {n, 1, z}] (* A008483 *)
Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, 2] == Length[p]], {n, 1, z}] (* A239493 *)
Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, 3] == Length[p]], {n, 1, z}] (* A239494 *)
Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, 4] == Length[p]], {n, 1, z}] (* A239495 *)
Table[Count[IntegerPartitions[n], p_ /; 2 Count[p, 5] == Length[p]], {n, 1, z}] (* A239496 *)


CROSSREFS

Cf. A230467, A008483, A239493, A239494, A239495.
Sequence in context: A124229 A055377 A157524 * A299962 A128586 A130971
Adjacent sequences: A239493 A239494 A239495 * A239497 A239498 A239499


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Mar 20 2014


STATUS

approved



