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%I #107 Jul 10 2021 10:25:31
%S 3,5,7,13,17,27,33,47,55,73,83,105,117,143,157,187,203,237,255,293,
%T 313,355,377,423,447,497,523,577,605,663,693,755,787,853,887,957,993,
%U 1067,1105,1183,1223,1305,1347,1433,1477,1567,1613,1707,1755,1853,1903
%N Numbers of the form 3*z^2 + z + 3 for some integer z.
%C Note that z is allowed to be negative. - _N. J. A. Sloane_, Jul 09 2021
%C Subsequence of A134407.
%C Numbers k such that 12*k - 35 is a square. - _Robert Israel_, Sep 18 2014
%H Colin Barker, <a href="/A247018/b247018.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F From _Colin Barker_, Feb 01 2018: (Start)
%F G.f.: x*(3 + 2*x - 4*x^2 + 2*x^3 + 3*x^4) / ((1 - x)^3*(1 + x)^2).
%F a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>5. (End)
%p select(t -> issqr(12*t-35), [$1..1000]); # _Robert Israel_, Sep 18 2014
%t 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 *)
%o (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
%Y Cf. A002522, A001105.
%K nonn,easy
%O 1,1
%A _Matt C. Anderson_, Sep 09 2014
%E 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.