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A247018
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Numbers of the form 3*z^2 + z + 3 for some integer z.
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1
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3, 5, 7, 13, 17, 27, 33, 47, 55, 73, 83, 105, 117, 143, 157, 187, 203, 237, 255, 293, 313, 355, 377, 423, 447, 497, 523, 577, 605, 663, 693, 755, 787, 853, 887, 957, 993, 1067, 1105, 1183, 1223, 1305, 1347, 1433, 1477, 1567, 1613, 1707, 1755, 1853, 1903
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OFFSET
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1,1
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COMMENTS
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Numbers k such that 12*k - 35 is a square. - Robert Israel, Sep 18 2014
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LINKS
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FORMULA
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G.f.: x*(3 + 2*x - 4*x^2 + 2*x^3 + 3*x^4) / ((1 - x)^3*(1 + x)^2).
a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>5. (End)
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MAPLE
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select(t -> issqr(12*t-35), [$1..1000]); # Robert Israel, Sep 18 2014
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MATHEMATICA
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Union[Flatten[Table[3z^2+{z, -z}+3, {z, 0, 40}]]] (* or *) LinearRecurrence[ {1, 2, -2, -1, 1}, {3, 5, 7, 13, 17}, 60] (* Harvey P. Dale, Jul 10 2021 *)
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PROG
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(PARI) Vec(x*(3 + 2*x - 4*x^2 + 2*x^3 + 3*x^4) / ((1 - x)^3*(1 + x)^2) + O(x^60)) \\ Colin Barker, Feb 01 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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At some point in the history of this entry the definition was changed from the correct definition to the erroneous "a(n) = 3*n^2 + n + 3". I have restored the original definition, and I deleted some incorrect programs. Thanks to Harvey P. Dale for pointing out that something was wrong. - N. J. A. Sloane, Jul 09 2021.
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STATUS
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approved
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