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 A260669 Number of unordered pairs of partitions of n with no common parts. 3
 0, 1, 2, 6, 8, 24, 30, 74, 110, 219, 309, 651, 870, 1608, 2394, 4085, 5756, 9931, 13785, 22724, 32300, 50404, 70862, 111540, 153756, 232868, 326259, 484090, 667015, 986082, 1345566, 1951216, 2673588, 3805742, 5179213, 7348514, 9895254, 13845750, 18681896 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..5000 FORMULA a(n) = A054440(n) / 2. EXAMPLE n = 6 has A000041(6) = 11 partitions: [6], [5,1], [4,2], [4,1,1], [3,3], [3,2,1], [3,1,1,1], [2,2,2], [2,2,1,1], [2,1,1,1,1], [1,1,1,1,1,1]; the following table shows the number of common parts of the pairs of these partitions, e.g. row i, col f: number of common parts of [2,2,1,1] and [3,2,1] = 2: . -------------------+---+---+---+---+---+---+---+---+---+---+---+ .                    | a | b | c | d | e | f | g | h | i | j | k | . ---+---------------+---+---+---+---+---+---+---+---+---+---+---+ .  a | [6]           | 1                                         | .  b | [5,1]         | 0   2                                     | .  c | [4,2]         | 0   0   2                                 | .  d | [4,1,1]       | 0   1   1   3                             | .  e | [3,3]         | 0   0   0   0   2                         | .  f | [3,2,1]       | 0   1   1   1   1   3                     | .  g | [3,1,1,1]     | 0   1   0   2   1   2   4                 | .  h | [2,2,2]       | 0   0   1   0   0   1   0   3             | .  i | [2,2,1,1]     | 0   1   1   2   0   2   2   2   4         | .  j | [2,1,1,1,1]   | 0   1   1   2   0   2   3   1   3   5     | .  k | [1,1,1,1,1,1] | 0   1   0   2   0   1   3   0   2   4   6 | . ---+---------------+---+---+---+---+---+---+---+---+---+---+---+ The table contains 24 zeros, therefore a(6) = 24. PROG (Haskell) a260669 = flip div 2 . a054440 CROSSREFS Cf. A000041, A054440. Sequence in context: A081957 A334901 A279732 * A122758 A122756 A193946 Adjacent sequences:  A260666 A260667 A260668 * A260670 A260671 A260672 KEYWORD nonn AUTHOR Reinhard Zumkeller, Nov 15 2015 STATUS approved

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Last modified April 13 11:56 EDT 2021. Contains 342936 sequences. (Running on oeis4.)