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A326657
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a(n) = 4*floor(n/2) + ceiling((n-1)^2/2).
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2
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1, 0, 5, 6, 13, 16, 25, 30, 41, 48, 61, 70, 85, 96, 113, 126, 145, 160, 181, 198, 221, 240, 265, 286, 313, 336, 365, 390, 421, 448, 481, 510, 545, 576, 613, 646, 685, 720, 761, 798, 841, 880, 925, 966, 1013, 1056, 1105, 1150, 1201, 1248, 1301, 1350, 1405, 1456, 1513, 1566, 1625, 1680
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OFFSET
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0,3
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COMMENTS
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a(n) gives the maximum number of inversions in a permutation on n + 2 symbols consisting of a single n-cycle and 2 fixed points.
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LINKS
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FORMULA
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a(n) = 4*floor(n/2) + ceiling((n-1)^2/2).
a(n) = A326296(2 + n, n) for n > 0.
G.f.: (1 - 2*x + 5*x^2 - 2*x^3) / ((1 - x)^3*(1 + x)).
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n >= 4.
a(n) = (-1 + 5*(-1)^n + 4*n + 2*n^2) / 4.
(End)
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PROG
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(PARI) a(n) = 4*floor(n/2) + ceil((n-1)^2/2) \\ Andrew Howroyd, Sep 23 2019
(PARI) Vec((1 - 2*x + 5*x^2 - 2*x^3) / ((1 - x)^3*(1 + x)) + O(x^40)) \\ Andrew Howroyd, Sep 23 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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