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A102344
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Numbers n such that the Diophantine equation (x+2)^3-x^3=2*n^2 has solutions.
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2
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2, 7, 97, 1351, 18817, 262087, 3650401, 50843527, 708158977, 9863382151, 137379191137, 1913445293767, 26650854921601, 371198523608647, 5170128475599457, 72010600134783751, 1002978273411373057, 13969685227624439047, 194572614913330773601, 2710046923559006391367
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OFFSET
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1,1
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COMMENTS
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n^2 = 3*(2*x+4)^2+16.
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LINKS
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FORMULA
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a(n+2) = 14*a(n+1)-a(n) for n>=2.
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EXAMPLE
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The first examples are 2^3-0^3=2*2^2 ; 5^3-3^3=2*7^2 ; 57^3-55^3=2*97^2 ; 781^3-779^3=2*1351^2 ; 10865^3-10863^3=2*18817^2
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MAPLE
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MATHEMATICA
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a[1]=2; a[2]=7; a[3]=97; a[n_] := a[n] = 14*a[n-1]-a[n-2]; Table[a[n], {n, 1, 17}] (* Jean-François Alcover, Dec 17 2013 *)
LinearRecurrence[{14, -1}, {2, 7, 97}, 20] (* Harvey P. Dale, Sep 26 2016 *)
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PROG
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(Magma) I:=[2, 7, 97]; [n le 3 select I[n] else 14*Self(n-1)-Self(n-2): n in [1..30]]; // Vincenzo Librandi, Apr 19 2015
(PARI) Vec(x*(2-21*x+x^2)/(1-14*x+x^2) + O(x^30)) \\ Michel Marcus, Apr 19 2015
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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