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%I #37 Sep 08 2022 08:45:55
%S -1,9,43,101,183,289,419,573,751,953,1179,1429,1703,2001,2323,2669,
%T 3039,3433,3851,4293,4759,5249,5763,6301,6863,7449,8059,8693,9351,
%U 10033,10739,11469,12223,13001,13803,14629,15479,16353,17251,18173,19119,20089,21083,22101,23143,24209
%N a(n) = 12*n^2 - 2*n - 1.
%C The second quadrisection of A184005(n-1) is A179741(n).
%C The first quadrisection of A184005(n-1) is a(n).
%C Sequence found by reading the line from -1, in the direction -1, 9, ..., in the square spiral whose vertices are -1 together with the generalized octagonal numbers A001082. - _Omar E. Pol_, Jul 18 2012
%H G. C. Greubel, <a href="/A185918/b185918.txt">Table of n, a(n) for n = 0..5000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = A184005(4*n-1). [corrected by _R. J. Mathar_, Aug 24 2011]
%F a(n) = a(n-1) + 24*n - 14.
%F a(n) = 2*a(n-1) - a(n) + 24.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F G.f.: -(1+x)*(13*x-1) / (x-1)^3. - _R. J. Mathar_, Aug 24 2011
%F a(n) = A154106(n-1) - 2, n >= 1. - _Omar E. Pol_, Jul 19 2012
%F E.g.f.: (12*x^2 + 10*x -1)*exp(x). - _G. C. Greubel_, Jul 22 2017
%p A185918:=n->12*n^2-2*n-1: seq(A185918(n), n=0..60); # _Wesley Ivan Hurt_, Jan 31 2017
%t Table[12n^2-2n-1,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{-1,9,43},50] (* _Harvey P. Dale_, May 20 2012 *)
%o (Magma) [-1-2*n+12*n^2: n in [0..80] ]; // _Vincenzo Librandi_, Feb 09 2011
%o (PARI) a(n)=12*n^2-2*n-1 \\ _Charles R Greathouse IV_, Dec 21 2011
%Y Cf. A001082, A154106, A179741, A184005.
%K sign,easy
%O 0,2
%A _Paul Curtz_, Feb 08 2011
%E More terms from _Vincenzo Librandi_, Feb 09 2011
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