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A154254
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a(n) = 9n^2 - 8n + 2.
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4
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2, 3, 22, 59, 114, 187, 278, 387, 514, 659, 822, 1003, 1202, 1419, 1654, 1907, 2178, 2467, 2774, 3099, 3442, 3803, 4182, 4579, 4994, 5427, 5878, 6347, 6834, 7339, 7862, 8403, 8962, 9539, 10134, 10747, 11378, 12027, 12694, 13379, 14082, 14803, 15542
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OFFSET
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0,1
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COMMENTS
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The identity (81*n^2 + 90*n + 26)^2 - (9*n^2 + 10*n + 3)*(27*n + 15)^2 = 1 can be written as A154277(n+1)^2 - a(n+1)*A154267(n)^2 = 1. - Vincenzo Librandi, Feb 03 2012
For n >= 1, the continued fraction expansion of sqrt(a(n)) is [3n-2; {1, 2, 3n-2, 2, 1, 6n-4}]. For n=1, this collapses to [1; {1, 2}]. - Magus K. Chu, Sep 09 2022
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LINKS
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FORMULA
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G.f.: (2 - 3*x + 19*x^2)/(1-x)^3.
a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). (End)
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MATHEMATICA
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PROG
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(Magma) I:=[2, 3, 22]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jan 29 2012
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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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