A105843 Numbers n such that n^2 = 37*m^2 + 37*m +1.

1, 149, 295, 21755, 43069, 3176081, 6287779, 463686071, 917972665, 67694990285, 134017721311, 9883004895539, 19565669338741, 1442851019758409, 2856453705734875, 210646365879832175, 417022675367953009, 30752926567435739141, 60882454150015404439

Offset

1,2

Links

Table of n, a(n) for n=1..19.

Index entries for linear recurrences with constant coefficients, signature (0,146,0,-1).

Formula

Define a(1)=1, a(2)=149, a(3)=146*a(1)+a(2), a(4)=146*a(2)+a(1), then a(n)=146*a(n-2)-a(n-4).

G.f.: x*(x+1)*(x^2+148*x+1) / ((x^2-12*x-1)*(x^2+12*x-1)). [Colin Barker, Mar 06 2013]

Mathematica

LinearRecurrence[{0, 146, 0, -1}, {1, 149, 295, 21755}, 20] (* Harvey P. Dale, Sep 17 2023 *)

Crossrefs

Cf. A105844 (associated m).

Sequence in context: A127592 A107176 A140023 * A131573 A346891 A244661

Adjacent sequences: A105840 A105841 A105842 * A105844 A105845 A105846

Keyword

nonn,easy

Author

Pierre CAMI, Apr 22 2005

Extensions

a(12)-a(19) from Colin Barker, Mar 06 2013

Status

approved