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A144965
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a(n)= 4*n*(4*n^2+1).
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2
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0, 20, 136, 444, 1040, 2020, 3480, 5516, 8224, 11700, 16040, 21340, 27696, 35204, 43960, 54060, 65600, 78676, 93384, 109820, 128080, 148260, 170456, 194764, 221280, 250100, 281320, 315036, 351344, 390340, 432120, 476780, 524416, 575124
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OFFSET
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0,2
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COMMENTS
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(a(n))^2 + (n*a(n)+1)^2 is always a perfect square.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Luc Comeau-Montasse, Des mesures entieres pour des triangles rectangles
Index to sequences with linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
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G.f.: 4*x*(5+14*x+5*x^2)/(1-x)^4. [Colin Barker, May 24 2012]
a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - Vincenzo Librandi, Jun 30 2012
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EXAMPLE
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Example : n = 181, a(n) = 94876580 (94876580^2 + (94876580*181 + 1)^2) = 17172923069.
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MATHEMATICA
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CoefficientList[Series[4*x*(5+14*x+5*x^2)/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 30 2012 *)
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PROG
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(MAGMA) I:=[0, 20, 136, 444]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jun 30 2012
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CROSSREFS
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Sequence in context: A168178 A085284 A105573 * A140301 A134382 A105939
Adjacent sequences: A144962 A144963 A144964 * A144966 A144967 A144968
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KEYWORD
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easy,nonn
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AUTHOR
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Luc Comeau-Montasse, Sep 27 2008
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STATUS
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approved
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