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 A239485 Number of (5,0)-separable partitions of n; see Comments. 4
 0, 1, 1, 2, 2, 2, 2, 4, 4, 6, 7, 8, 9, 12, 13, 16, 19, 22, 25, 31, 34, 41, 47, 54, 62, 74, 82, 96, 110, 126, 143, 167, 187, 216, 245, 279, 316, 364, 408, 466, 527, 597, 673, 767, 860, 976, 1098, 1238, 1391, 1574, 1761, 1986, 2228, 2502, 2801, 3150, 3518 (list; graph; refs; listen; history; text; internal format)
 OFFSET 6,4 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 (5,0)-separable partitions of 13 are 751, 652, 454, 15151, so that a(13) = 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, A239481, A165652, A239483, A239484. Sequence in context: A325710 A214927 A326115 * A237756 A010334 A010578 Adjacent sequences:  A239482 A239483 A239484 * A239486 A239487 A239488 KEYWORD nonn,easy AUTHOR Clark Kimberling, Mar 20 2014 STATUS approved

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Last modified August 12 23:19 EDT 2020. Contains 336440 sequences. (Running on oeis4.)