A105845 Numbers n such that n^2 = 41*m^2 + 41*m + 1.

1, 4511, 8609, 18486079, 35279681, 75755947231, 144576124129, 310447853266559, 592472921400961, 1272215226930411551, 2427953887325014049, 5213537689512973269439, 9949754437784986171841, 21365076179408937527749471, 40774091258088986007190369

Offset

1,2

Links

Table of n, a(n) for n=1..15.

Index entries for linear recurrences with constant coefficients, signature (0,4098,0,-1).

Formula

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).

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]

Mathematica

CoefficientList[Series[x(x+1)(x^2+4510x+1)/((x^2-64x-1)(x^2+64x-1)), {x, 0, 20}], x] (* or *) LinearRecurrence[{0, 4098, 0, -1}, {0, 1, 4511, 8609, 18486079}, 30] (* Harvey P. Dale, Jul 05 2022 *)

Crossrefs

Cf. A105846 (associated m).

Sequence in context: A252628 A252623 A023684 * A107543 A234425 A209955

Adjacent sequences: A105842 A105843 A105844 * A105846 A105847 A105848

Keyword

nonn,easy

Author

Pierre CAMI, Apr 22 2005

Extensions

a(10)-a(15) from Colin Barker, Mar 06 2013

Status

approved