login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 h-separable 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 12 17:59 EST 2019. Contains 329960 sequences. (Running on oeis4.)