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A216053
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a(n) is the position of the last two-tuple within the reverse lexicographic set of partitions of 2n and 2n+1, with a(1)-a(n) representing the positions of every 2-tuple partition of 2n and 2n+1.
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5
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2, 3, 5, 8, 13, 20, 31, 46, 68, 98, 140, 196, 273, 374, 509, 685, 916, 1213, 1598, 2088, 2715, 3507, 4509, 5764, 7339, 9297, 11733, 14743, 18461, 23026, 28630, 35472, 43821, 53964, 66274, 81157, 99134, 120771, 146786, 177971, 215309, 259892, 313066, 376327
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) ~ exp(Pi*sqrt(2*n/3)) / (Pi*2^(3/2)*sqrt(n)). - Vaclav Kotesovec, May 24 2018
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EXAMPLE
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With n = 3, 2n = 6. The partitions of 6 are {{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 last 2-tuple is located at position 5. The positions of all 2-tuples are 2, 3, and 5.
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MATHEMATICA
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RecurrenceTable[{a[n+1] == a[n] + PartitionsP[(n)], a[1] == 2}, a, {n, 1, 44}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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