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%I #30 Sep 08 2022 08:45:38
%S 1,22,75,160,277,426,607,820,1065,1342,1651,1992,2365,2770,3207,3676,
%T 4177,4710,5275,5872,6501,7162,7855,8580,9337,10126,10947,11800,12685,
%U 13602,14551,15532,16545,17590,18667,19776,20917,22090,23295,24532
%N Ulam's spiral (SSW spoke).
%C Also sequence found by reading the segment (1, 22) together with the line from 22, in the direction 22, 75, ..., in the square spiral whose vertices are the generalized decagonal numbers A074377. - _Omar E. Pol_, Nov 05 2012
%H G. C. Greubel, <a href="/A143838/b143838.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = 16*n^2 - 27*n + 12, n>0. - _R. J. Mathar_, Sep 04 2008
%F G.f.: x*(1 + 19*x + 12*x^2)/(1-x)^3. - _Colin Barker_, Aug 03 2012
%F E.g.f.: -12 + (12 - 11*x + 16*x^2)*exp(x). - _G. C. Greubel_, Nov 09 2019
%p seq( ((32*n-27)^2 +39)/64, n=1..50); # _G. C. Greubel_, Nov 09 2019
%t f[n_]:= 16n^2 -27n +12; Array[f, 40] (* _Vladimir Joseph Stephan Orlovsky_, Sep 02 2008 *)
%t CoefficientList[Series[(1+19x+12x^2)/(1-x)^3, {x, 0, 40}], x] (* _Vincenzo Librandi_, Nov 08 2014 *)
%t ((32*Range[50]-27)^2 +39)/64 (* _G. C. Greubel_, Nov 09 2019 *)
%t LinearRecurrence[{3,-3,1},{1,22,75},40] (* _Harvey P. Dale_, Sep 26 2020 *)
%o (Magma) [16*n^2-27*n+12: n in [1..50]]; // _Vincenzo Librandi_, Nov 08 2014
%o (PARI) vector(50, n, 16*n^2-27*n+12) \\ _Michel Marcus_, Nov 08 2014
%o (Sage) [((32*n-27)^2 +39)/64 for n in (1..50)] # _G. C. Greubel_, Nov 09 2019
%o (GAP) List([1..50], n-> ((32*n-27)^2 +39)/64); # _G. C. Greubel_, Nov 09 2019
%K nonn,easy
%O 1,2
%A _Vladimir Joseph Stephan Orlovsky_, Sep 02 2008
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