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A156676
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a(n) = 81*n^2 - 44*n + 6.
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5
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6, 43, 242, 603, 1126, 1811, 2658, 3667, 4838, 6171, 7666, 9323, 11142, 13123, 15266, 17571, 20038, 22667, 25458, 28411, 31526, 34803, 38242, 41843, 45606, 49531, 53618, 57867, 62278, 66851, 71586, 76483, 81542, 86763, 92146, 97691, 103398
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OFFSET
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0,1
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COMMENTS
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The identity (6561*n^2 - 3564*n + 485)^2 - (81*n^2 - 44*n + 6)*(729*n - 198)^2 = 1 can be written as A156774(n)^2 - a(n)* A156772(n)^2 = 1 for n > 0.
For n >= 1, the continued fraction expansion of sqrt(a(n)) is [9n-3; {1, 1, 3, 1, 9n-4, 1, 3, 1, 1, 18n-6}]. - Magus K. Chu, Sep 13 2022
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LINKS
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FORMULA
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a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: (6 + 25*x + 131*x^2)/(1-x)^3.
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MAPLE
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {6, 43, 242}, 40]
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PROG
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(Magma) [81*n^2 - 44*n + 6: n in [0..40] ]
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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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EXTENSIONS
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STATUS
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approved
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