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A143860 Ulam's spiral (NNW spoke).

%I A143860 #31 Sep 08 2022 08:45:38
%S A143860 1,16,63,142,253,396,571,778,1017,1288,1591,1926,2293,2692,3123,3586,
%T A143860 4081,4608,5167,5758,6381,7036,7723,8442,9193,9976,10791,11638,12517,
%U A143860 13428,14371,15346,16353,17392,18463,19566,20701,21868,23067,24298
%N A143860 Ulam's spiral (NNW spoke).
%C A143860 Also, except for the first term, sequence found by reading the line from 16, in the direction 16, 63,... in the square spiral whose vertices are the generalized decagonal numbers A074377. - _Omar E. Pol_, Nov 05 2012
%H A143860 Vincenzo Librandi, <a href="/A143860/b143860.txt">Table of n, a(n) for n = 1..1000</a>
%H A143860 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A143860 a(n) = 16*n^2 - 33*n + 18. - _R. J. Mathar_, Sep 08 2008
%F A143860 G.f. x*(1 + 13*x + 18*x^2)/(1-x)^3. - _R. J. Mathar_, Oct 31 2011
%F A143860 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Jul 10 2012
%F A143860 E.g.f.: -18 + (18 - 17*x + 16*x^2)*exp(x). - _G. C. Greubel_, Nov 09 2019
%p A143860 seq( ((32*n-33)^2 +63)/64, n=1..40); # _G. C. Greubel_, Nov 09 2019
%t A143860 f[n_]:= 16n^2 -33n +18; Array[f, 40] (* _Robert G. Wilson v_, Oct 31 2011 *)
%t A143860 ((32*Range[50]-33)^2 +63)/64 (* _G. C. Greubel_, Nov 09 2019 *)
%o A143860 (Magma) [16*n^2-33*n+18: n in [1..40]]; // _Vincenzo Librandi_, Jul 10 2012
%o A143860 (PARI) a(n)=16*n^2-33*n+18 \\ _Charles R Greathouse IV_, Jun 17 2017
%o A143860 (Sage) [((32*n-33)^2 +63)/64 for n in (1..40)] # _G. C. Greubel_, Nov 09 2019
%o A143860 (GAP) List([1..40], n-> ((32*n-33)^2 +63)/64); # _G. C. Greubel_, Nov 09 2019
%K A143860 nonn,easy
%O A143860 1,2
%A A143860 _Vladimir Joseph Stephan Orlovsky_, Sep 03 2008