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A170837
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a(0)=0, a(1)=1 and a(n) = 16n-27 for n >= 2.
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3
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0, 1, 5, 21, 37, 53, 69, 85, 101, 117, 133, 149, 165, 181, 197, 213, 229, 245, 261, 277, 293, 309, 325, 341, 357, 373, 389, 405, 421, 437, 453, 469, 485, 501, 517, 533, 549, 565, 581, 597, 613, 629, 645, 661, 677, 693, 709, 725, 741, 757, 773, 789, 805
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OFFSET
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0,3
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,-1).
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FORMULA
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G.f.: x*(3*x+12*x^2+1)/(x-1)^2.
a(n) = 2*a(n-1) -a(n-2), n>=4.
a(n) = 4*A016813(n-2) + 1, n>=2. - Ivan N. Ianakiev, Jul 20 2013
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MATHEMATICA
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CoefficientList[Series[x*(3*x + 12*x^2 + 1)/(x - 1)^2, {x, 0, 60}], x] (* Vincenzo Librandi, Dec 19 2012 *)
LinearRecurrence[{2, -1}, {0, 1, 5, 21}, 60] (* Harvey P. Dale, Oct 09 2017 *)
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PROG
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(Magma) I:=[0, 1, 5, 21]; [n le 4 select I[n] else 2*Self(n-1) - Self(n-2): n in [1..60]]; // Vincenzo Librandi, Dec 19 2012
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CROSSREFS
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Cf. A170836 (first differences), A170876.
Sequence in context: A039561 A063575 A302873 * A170876 A341198 A038844
Adjacent sequences: A170834 A170835 A170836 * A170838 A170839 A170840
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Jan 05 2010, based on email from R. J. Mathar and Benoit Jubin, Jun 02 2009; revised Jan 09 2010
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STATUS
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approved
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