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A108928
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a(n) = 8*n^2 - 3.
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3
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5, 29, 69, 125, 197, 285, 389, 509, 645, 797, 965, 1149, 1349, 1565, 1797, 2045, 2309, 2589, 2885, 3197, 3525, 3869, 4229, 4605, 4997, 5405, 5829, 6269, 6725, 7197, 7685, 8189, 8709, 9245, 9797, 10365, 10949, 11549, 12165, 12797, 13445, 14109, 14789
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OFFSET
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1,1
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COMMENTS
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Sequence found by reading the segment (5, 29) together with the line from 29, in the direction 29, 69,..., in the square spiral whose vertices are the triangular numbers A000217. - Omar E. Pol, Sep 04 2011
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n) = 2*(2*n-1)*(2*n+1)-1.
a(1)=5, a(2)=29, a(3)=69, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Jul 21 2012
From G. C. Greubel, Jul 15 2017:(Start)
G.f.: x*(-5 - 14*x + 3*x^2)/(-1 + x)^3.
E.g.f.: (8*x^2 + 8*x - 3)*exp(x) + 3. (End)
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EXAMPLE
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(1*3 = 3)+2 = 5; (3*5 = 15)+14 = 29; (5*7 = 35)+34 = 69; (7*9 = 63)+62 = 125; ...
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MAPLE
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seq(8*n^2-3, n=1..50); # Emeric Deutsch, Aug 01 2005
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MATHEMATICA
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8*Range[50]^2-3 (* or *) LinearRecurrence[{3, -3, 1}, {5, 29, 69}, 50] (* Harvey P. Dale, Jul 21 2012 *)
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PROG
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(PARI) a(n)=8*n^2-3 \\ Charles R Greathouse IV, Sep 04 2011
(MAGMA) [8*n^2 - 3: n in [1..50]]; // Vincenzo Librandi, Sep 05 2011
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CROSSREFS
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Sequence in context: A341085 A301858 A293174 * A097812 A176333 A100559
Adjacent sequences: A108925 A108926 A108927 * A108929 A108930 A108931
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KEYWORD
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easy,nonn
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AUTHOR
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Marcel Hetkowski Fabeny (marcelfabeny(AT)yahoo.com.br), Jul 19 2005
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EXTENSIONS
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More terms from Emeric Deutsch, Aug 01 2005
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STATUS
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approved
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