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A179805
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a(0) = 1, a(1) = 3, a(2) = 6 and a(n) = 2*a(n-1) - a(n-2) for n > 3.
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6
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1, 3, 6, 15, 24, 33, 42, 51, 60, 69, 78, 87, 96, 105, 114, 123, 132, 141, 150, 159, 168, 177, 186, 195, 204, 213, 222, 231, 240, 249, 258, 267, 276, 285, 294, 303, 312, 321, 330, 339, 348, 357, 366, 375, 384, 393, 402
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OFFSET
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0,2
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COMMENTS
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For n > 1, a(n) is the maximum value of the sum of the vertices in a normal magic triangle of order n (see formula 10 in Trotter). - Stefano Spezia, Mar 03 2021
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LINKS
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FORMULA
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(1 + 3*x + 6*x^2 + 15*x^3 + ...) = (1 + 3*x^2 + 3*x^3 + 3*x^4 + ...) * (1 + 3*x + 3*x^2 + 3*x^3 + 3*x^4 + ...).
a(0) = 1, a(1) = 3, a(2) = 6 and a(n) = 2*a(n-1) - a(n-2) for n > 3.
a(n) = a(n-1) + 9 for n > 2.
For n > 1, a(n) == 6 (mod 9).
a(n) = 9*n - 12 for n > 1.
G.f.: (2*x+1)*(3*x^2-x+1)/(x-1)^2. (End)
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EXAMPLE
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a(4) = 24 = 9 + a(3) = 9 + 15.
a(4) = 24 = 2*a(3) - a(2) = 2*15 - 6.
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MATHEMATICA
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LinearRecurrence[{2, -1}, {1, 3, 6, 15}, 50] (* Harvey P. Dale, Sep 25 2018 *)
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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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