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A158058
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a(n) = 16*n^2 - 2*n.
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2
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14, 60, 138, 248, 390, 564, 770, 1008, 1278, 1580, 1914, 2280, 2678, 3108, 3570, 4064, 4590, 5148, 5738, 6360, 7014, 7700, 8418, 9168, 9950, 10764, 11610, 12488, 13398, 14340, 15314, 16320, 17358, 18428, 19530, 20664, 21830, 23028, 24258, 25520
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OFFSET
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1,1
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COMMENTS
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The identity (16*(n-1) + 15)^2 - (16*n^2 - 2*n)*4^2 = 1 can be written as A125169(n-1)^2 - a(n)*4^2 = 1. - Vincenzo Librandi, Feb 01 2012
Sequence found by reading the line from 14, in the direction 14, 60, ... in the square spiral whose vertices are the generalized decagonal numbers A074377. - Omar E. Pol, Nov 02 2012
The continued fraction expansion of sqrt(a(n)) is [4n-1; {1, 2, 1, 8n-2}]. - Magus K. Chu, Nov 08 2022
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LINKS
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FORMULA
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G.f.: x*(-14 - 18*x)/(x-1)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
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MAPLE
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {14, 60, 138}, 40]
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PROG
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(Magma) [16*n^2-2*n: n in [1..40]]
(PARI) a(n) = 16*n^2-2*n.
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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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