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 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 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

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