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 A239482 Number of (2,0)-separable partitions of n; see Comments. 18
 0, 1, 0, 1, 2, 2, 3, 5, 5, 7, 10, 11, 14, 19, 21, 27, 34, 39, 48, 60, 69, 84, 102, 119, 142, 172, 199, 237, 282, 328, 387, 458, 530, 623, 730, 847, 987, 1153, 1331, 1547, 1796, 2071, 2394, 2771, 3183, 3671, 4227, 4849, 5568, 6395, 7313, 8377, 9584, 10940 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,5 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 (2,0)-separable partitions of 10 are 721, 523, 424, 42121, 1212121, so that a(10) = 5. 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, A239483, A239484, A239485. Sequence in context: A033189 A008507 A028364 * A280470 A011971 A060048 Adjacent sequences:  A239479 A239480 A239481 * A239483 A239484 A239485 KEYWORD nonn,easy AUTHOR Clark Kimberling, Mar 20 2014 STATUS approved

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