A143856 - OEIS

%I #29 Sep 02 2024 11:53:53

%S 1,12,55,130,237,376,547,750,985,1252,1551,1882,2245,2640,3067,3526,

%T 4017,4540,5095,5682,6301,6952,7635,8350,9097,9876,10687,11530,12405,

%U 13312,14251,15222,16225,17260,18327,19426,20557,21720,22915,24142

%N Ulam's spiral (ENE spoke).

%C Also sequence found by reading the segment (1, 12) together with the line from 12, in the direction 12, 55,..., in the square spiral whose vertices are the generalized decagonal numbers A074377. - _Omar E. Pol_, Nov 05 2012

%H Vincenzo Librandi, <a href="/A143856/b143856.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 - 37*n + 22. - _R. J. Mathar_, Sep 08 2008

%F G.f. x*(1 + 9*x + 22*x^2)/(1-x)^3. - _R. J. Mathar_, Oct 31 2011

%F a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - _Vincenzo Librandi_, Jul 10 2012

%F E.g.f.: -22 + (22 - 21*x + 16*x^2)*exp(x). - _G. C. Greubel_, Nov 09 2019

%p seq( ((32*n-37)^2 +39)/64, n=1..40); # _G. C. Greubel_, Nov 09 2019

%t f[n_]:= 16n^2 -37n +22; Array[f, 40] (* _Robert G. Wilson v_, Oct 31 2011 *)

%t Table[16n^2-37*n+22,{n,1,40}] (* _Vincenzo Librandi_, Jul 10 2012 *)

%t LinearRecurrence[{3,-3,1},{1,12,55},50] (* _Harvey P. Dale_, Sep 02 2024 *)

%o (Magma) [16*n^2 -37*n +22: n in [1..40]]; // _Vincenzo Librandi_, Jul 10 2012

%o (PARI) a(n)=16*n^2-37*n+22 \\ _Charles R Greathouse IV_, Jun 17 2017

%o (Sage) [((32*n-37)^2 +39)/64 for n in (1..40)] # _G. C. Greubel_, Nov 09 2019

%o (GAP) List([1..40], n-> ((32*n-37)^2 +39)/64); # _G. C. Greubel_, Nov 09 2019

%K nonn,easy

%O 1,2

%A _Vladimir Joseph Stephan Orlovsky_, Sep 03 2008