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A143855 Ulam's spiral (ESE spoke).

%I A143855 #31 Sep 08 2022 08:45:38
%S A143855 1,10,51,124,229,366,535,736,969,1234,1531,1860,2221,2614,3039,3496,
%T A143855 3985,4506,5059,5644,6261,6910,7591,8304,9049,9826,10635,11476,12349,
%U A143855 13254,14191,15160,16161,17194,18259,19356,20485,21646,22839,24064
%N A143855 Ulam's spiral (ESE spoke).
%C A143855 Also sequence found by reading the segment (1, 10) together with the line from 10, in the direction 10, 51, ..., in the square spiral whose vertices are the generalized decagonal numbers A074377. - _Omar E. Pol_, Nov 05 2012
%H A143855 G. C. Greubel, <a href="/A143855/b143855.txt">Table of n, a(n) for n = 1..1000</a>
%H A143855 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A143855 a(n) = 16*n^2 - 39*n + 24. - _R. J. Mathar_, Sep 08 2008
%F A143855 G.f.: x*(1 + 7*x + 24*x^2)/(1-x)^3. - _Colin Barker_, Aug 03 2012
%F A143855 E.g.f.: -24 + (24 - 23*x + 16*x^2)*exp(x). - _G. C. Greubel_, Nov 09 2019
%p A143855 seq( ((32*n -39)^2 +15)/64, n=1..50); # _G. C. Greubel_, Nov 09 2019
%t A143855 f[n_]:= 16n^2 -39n +24; Array[f, 40] (* _Vladimir Joseph Stephan Orlovsky_, Sep 04 2008 *)
%t A143855 CoefficientList[Series[(1+7x+24x^2)/(1-x)^3, {x,0,40}], x] (* _Vincenzo Librandi_, Nov 08 2014 *)
%t A143855 ((32*Range[50] -39)^2 +15)/64 (* _G. C. Greubel_, Nov 09 2019 *)
%o A143855 (Magma) [16*n^2-39*n+24: n in [1..50]]; // _Vincenzo Librandi_, Nov 08 2014
%o A143855 (PARI) vector(50, n, 16*n^2-39*n+24) \\ _Michel Marcus_, Nov 08 2014
%o A143855 (Sage) [((32*n-39)^2 +15)/64 for n in (1..50)] # _G. C. Greubel_, Nov 09 2019
%o A143855 (GAP) List([1..50], n-> ((32*n-39)^2 +15)/64); # _G. C. Greubel_, Nov 09 2019
%K A143855 nonn,easy
%O A143855 1,2
%A A143855 _Vladimir Joseph Stephan Orlovsky_, Sep 03 2008, Sep 04 2008