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A122571
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a(1)=a(2)=1, a(n) = 14*a(n-1) - a(n-2).
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2
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1, 1, 13, 181, 2521, 35113, 489061, 6811741, 94875313, 1321442641, 18405321661, 256353060613, 3570537526921, 49731172316281, 692665874901013, 9647591076297901, 134373609193269601, 1871582937629476513, 26067787517619401581, 363077442309042145621, 5057016404808970637113
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OFFSET
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1,3
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COMMENTS
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Each term is a sum of two consecutive squares, or a(n) = k^2 + (k+1)^2 for some k. Squares of each term are the hex numbers, or centered hexagonal numbers: a(n) = A001570(n-1) for n > 1. - Alexander Adamchuk, Apr 14 2008
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REFERENCES
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Henry MacKean and Victor Moll, Elliptic Curves, Cambridge University Press, New York, 1997, page 22.
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LINKS
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FORMULA
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a(n) = (1/4)*sqrt(2+(2-sqrt(3))^(4*n-2) + (2+sqrt(3))^(4*n-2)). - Gerry Martens, Jun 03 2015
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MATHEMATICA
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LinearRecurrence[{14, -1}, {1, 1}, 25] (* Paolo Xausa, Jan 29 2024 *)
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CROSSREFS
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Cf. A001570 (essentially the same).
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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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