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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: A214628 A032576 A276420 * A071809 A324762 A104976

Adjacent sequences:  A239491 A239492 A239493 * A239495 A239496 A239497

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 20 2014

STATUS

approved

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Last modified November 21 01:23 EST 2019. Contains 329348 sequences. (Running on oeis4.)