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18, 68, 150, 264, 410, 588, 798, 1040, 1314, 1620, 1958, 2328, 2730, 3164, 3630, 4128, 4658, 5220, 5814, 6440, 7098, 7788, 8510, 9264, 10050, 10868, 11718, 12600, 13514, 14460, 15438, 16448, 17490, 18564, 19670, 20808, 21978, 23180, 24414, 25680
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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)^2-(16*n^2+2*n)*(4)^2 = 1 can be written as A158057(n)^2-a(n)*(4)^2 = 1. - Vincenzo Librandi, Feb 09 2012
Sequence found by reading the line from 18, in the direction 18, 68,... in the square spiral whose vertices are the generalized decagonal numbers A074377. - Omar E. Pol, Nov 02 2012
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
G.f.: 2*x*(-9-7*x)/(x-1)^3
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {18, 68, 150}, 50]
Table[16n^2+2n, {n, 40}] (* From Harvey P. Dale, Apr 13 2011 *)
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PROG
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(MAGMA) I:=[18, 68, 150]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];
(PARI) a(n) = 16*n^2 + 2*n.
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CROSSREFS
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Cf. A158057.
Sequence in context: A143859 A063523 A045234 * A214491 A135470 A059224
Adjacent sequences: A158053 A158054 A158055 * A158057 A158058 A158059
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Mar 12 2009
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STATUS
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approved
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