The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A239494 Number of (3,1)-separable partitions of n; see Comments. 4
 0, 0, 0, 1, 1, 0, 1, 2, 2, 2, 2, 4, 4, 5, 6, 8, 9, 11, 13, 17, 19, 23, 27, 34, 39, 46, 54, 66, 76, 90, 104, 125, 144, 169, 196, 231, 266, 310, 358, 419, 480, 557, 640, 743, 851, 980, 1123, 1295, 1479, 1697, 1936, 2221, 2529, 2890, 3288, 3753, 4262, 4851 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 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..58. EXAMPLE The (3,1)-separable partitions of 14 are [11,3], [7,3,1,3], [6,3,2,3], [4,3,4,3], [2,3,2,3,1,3], so that a(14) = 5. 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, A239495, A239496. Sequence in context: A355806 A032576 A276420 * A349388 A347663 A071809 Adjacent sequences: A239491 A239492 A239493 * A239495 A239496 A239497 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 28 14:35 EDT 2023. Contains 365735 sequences. (Running on oeis4.)