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A143854 Ulam's spiral (WSW spoke).

%I A143854 #26 Sep 08 2022 08:45:38
%S A143854 1,20,71,154,269,416,595,806,1049,1324,1631,1970,2341,2744,3179,3646,
%T A143854 4145,4676,5239,5834,6461,7120,7811,8534,9289,10076,10895,11746,12629,
%U A143854 13544,14491,15470,16481,17524,18599,19706,20845,22016,23219,24454
%N A143854 Ulam's spiral (WSW spoke).
%C A143854 Also sequence found by reading the segment (1, 20) together with the line from 20, in the direction 20, 71, ..., in the square spiral whose vertices are the generalized decagonal numbers A074377. - _Omar E. Pol_, Nov 05 2012
%H A143854 G. C. Greubel, <a href="/A143854/b143854.txt">Table of n, a(n) for n = 1..1000</a>
%H A143854 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A143854 From _Colin Barker_, Aug 03 2012: (Start)
%F A143854 a(n) = 14 - 29*n + 16*n^2.
%F A143854 G.f.: x*(1 + 17*x + 14*x^2)/(1-x)^3. (End)
%F A143854 E.g.f.: -14 + (14 - 13*x + 16*x^2)*exp(x). - _G. C. Greubel_, Nov 09 2019
%p A143854 seq( ((32*n-29)^2 +55)/64, n=1..40); # _G. C. Greubel_, Nov 09 2019
%t A143854 f[n_]:= 16n^2 -29n +14; Array[f, 40] (* _Vladimir Joseph Stephan Orlovsky_, Sep 03 2008 *)
%t A143854 CoefficientList[Series[(1+17x+14x^2)/(1-x)^3, {x, 0, 40}], x] (* _Vincenzo Librandi_, Nov 08 2014 *)
%t A143854 ((32*Range[50] -29)^2 +55)/64 (* _G. C. Greubel_, Nov 09 2019 *)
%o A143854 (Magma) [14-29*n+16*n^2: n in [1..50]]; // _Vincenzo Librandi_, Nov 08 2014
%o A143854 (PARI) vector(50, n, 14-29*n+16*n^2) \\ _Michel Marcus_, Nov 08 2014
%o A143854 (Sage) [((32*n-29)^2 +55)/64 for n in (1..50)] # _G. C. Greubel_, Nov 09 2019
%o A143854 (GAP) List([1..50], n-> ((32*n-29)^2 +55)/64); # _G. C. Greubel_, Nov 09 2019
%K A143854 nonn,easy
%O A143854 1,2
%A A143854 _Vladimir Joseph Stephan Orlovsky_, Sep 03 2008