A105845 - OEIS

%I #13 Jun 30 2026 23:01:13

%S 1,4511,8609,18486079,35279681,75755947231,144576124129,

%T 310447853266559,592472921400961,1272215226930411551,

%U 2427953887325014049,5213537689512973269439,9949754437784986171841,21365076179408937527749471,40774091258088986007190369

%N Numbers n such that n^2 = 41*m^2 + 41*m + 1.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,4098,0,-1).

%F Define a(1)=1, a(2)=4511, a(3)=4098*a(1)+a(2), a(4)=4098*a(2)+a(1), then a(n)=4098*a(n-2)-a(n-4).

%F G.f.: x*(x+1)*(x^2+4510*x+1) / ((x^2-64*x-1)*(x^2+64*x-1)). [_Colin Barker_, Mar 06 2013]

%t CoefficientList[Series[x(x+1)(x^2+4510x+1)/((x^2-64x-1)(x^2+64x-1)),{x,0,20}],x] (* _Harvey P. Dale_, Jul 05 2022 *)

%t (* Alternative: *)

%t LinearRecurrence[{0,4098,0,-1},{0,1,4511,8609,18486079},30] (* _Harvey P. Dale_, Jul 05 2022 *)

%Y Cf. A105846 (associated m).

%K nonn,easy

%O 1,2

%A _Pierre CAMI_, Apr 22 2005

%E a(10)-a(15) from _Colin Barker_, Mar 06 2013