login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A239483 Number of (3,0)-separable partitions of n; see Comments. 4
0, 1, 1, 1, 1, 3, 3, 4, 5, 7, 8, 10, 12, 16, 18, 22, 26, 33, 38, 45, 53, 65, 75, 89, 103, 124, 143, 168, 195, 230, 265, 309, 357, 418, 479, 556, 639, 742, 850, 979, 1122, 1294, 1478, 1696, 1935, 2220, 2528, 2889, 3287, 3752, 4261, 4850, 5502, 6257, 7084 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,6

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=4..58.

EXAMPLE

The (3,0)-separable partitions of 11 are 731, 632, 434, 23231, so that a(11) = 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, A239484, A239485.

Sequence in context: A144489 A239640 A100091 * A104806 A241442 A043551

Adjacent sequences:  A239480 A239481 A239482 * A239484 A239485 A239486

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 August 6 18:25 EDT 2020. Contains 336256 sequences. (Running on oeis4.)