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 A239467 Number of 1-separable partitions of n; see Comments. 9
 0, 0, 1, 2, 3, 4, 6, 8, 11, 14, 19, 24, 31, 39, 50, 62, 78, 96, 120, 147, 181, 220, 270, 327, 397, 478, 578, 693, 833, 994, 1189, 1414, 1683, 1994, 2365, 2792, 3297, 3880, 4568, 5359, 6287, 7354, 8602, 10036, 11704, 13618, 15841, 18387, 21332, 24702, 28591 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 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 (1,0)-separable partitions of 7:  421, 313 (1,1)-separable partitions of 7:  61, 3121 (1,2)-separable partitions of 7:  151, 12121 1-separable partitions of 7:  421, 313, 61, 3121, 151, 12121, so that a(7) = 6. MATHEMATICA z = 55; t1 = -1 + Table[Count[IntegerPartitions[n], p_ /; Length[p] - 1 <= 2 Count[p, 1] <= Length[p] + 1], {n, 1, z}] (* A239467 *) t2 = -1 + Table[Count[IntegerPartitions[n], p_ /; Length[p] - 1 <= 2 Count[p, 2] <= Length[p] + 1], {n, 1, z}] (* A239468 *) t3 = -1 + Table[Count[IntegerPartitions[n], p_ /; Length[p] - 1 <= 2 Count[p, 3] <= Length[p] + 1], {n, 1, z}] (* A239469 *) t4 = -1 + Table[Count[IntegerPartitions[n], p_ /; Length[p] - 1 <= 2 Count[p, 4] <= Length[p] + 1], {n, 1, z}] (* A239470 *) t5 = -1 + Table[Count[IntegerPartitions[n], p_ /; Length[p] - 1 <= 2 Count[p, 5] <= Length[p] + 1], {n, 1, z}] (* A239472 *) CROSSREFS Cf. A239468, A239469, A239470, A239471. Sequence in context: A233693 A003412 A038348 * A035945 A094707 A303663 Adjacent sequences:  A239464 A239465 A239466 * A239468 A239469 A239470 KEYWORD nonn,easy AUTHOR Clark Kimberling, Mar 20 2014 STATUS approved

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Last modified October 22 14:44 EDT 2019. Contains 328318 sequences. (Running on oeis4.)