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%I #54 Feb 17 2023 14:57:34
%S 1,49,169,361,625,961,1369,1849,2401,3025,3721,4489,5329,6241,7225,
%T 8281,9409,10609,11881,13225,14641,16129,17689,19321,21025,22801,
%U 24649,26569,28561,30625,32761,34969,37249,39601,42025,44521,47089,49729,52441,55225
%N a(n) = (6*n+1)^2.
%C Except for 2, exponents e such that x^e-x+1 is reducible.
%H Vincenzo Librandi, <a href="/A016922/b016922.txt">Table of n, a(n) for n = 0..2000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F G.f.: ( 1+46*x+25*x^2 ) / (1-x)^3. - _R. J. Mathar_, Mar 10 2011
%F a(n) = A016921(n)^2 = A000290(A016921(n)). - _Wesley Ivan Hurt_, Dec 06 2013
%F a(n) = 24*A005449(n)+1. - _Jean-Bernard François_, Oct 12 2014
%F a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). - _Wesley Ivan Hurt_, Oct 13 2014
%F Sum_{n>=0} 1/a(n) = A086727. - _Amiram Eldar_, Nov 16 2020
%p A016922:=n->(6*n+1)^2; seq(A016922(n), n=0..100); # _Wesley Ivan Hurt_, Dec 06 2013
%t Table[(6n+1)^2, {n,0,100}] (* or *)
%t CoefficientList[Series[(1 + 46*x + 25*x^2)/(1 - x)^3, {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Oct 13 2014 *)
%t LinearRecurrence[{3,-3,1},{1,49,169},50] (* _Harvey P. Dale_, Feb 17 2023 *)
%o (Magma) [(6*n+1)^2: n in [0..60]]; // _Vincenzo Librandi_, May 04 2011
%o (PARI) a(n)=(6*n+1)^2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A000290, A005449, A086727, A016778 (bisection), A016921.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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