A105841 Numbers n such that n^2 = 31*m^2 + 31*m + 1.

1, 309, 50469, 8242961, 17484559, 2855704251, 466414209771, 76178131891679, 161585265485281, 26391270694632789, 4310412628191203589, 704007671333868620081, 1493306066338224434479, 243897514468974137852571, 39835100723866104291485451

Offset

1,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,9241598,0,0,0,-1).

Formula

a(1)=1, a(2)=309, a(3)=50469, a(4)=8242961, a(5)=9241598*a(1)+a(4), a(6)=9241598*a(2)+a(3), a(7)=9241598*a(3)+a(2), a(8)=9241598*a(4)=a(1), then a(n)=9241598*a(n-4)-a(n-8)

G.f.: x*(x+1)*(x^6+308*x^5+50161*x^4+8192800*x^3+50161*x^2+308*x+1) / ((x^4-3040*x^2+1)*(x^4+3040*x^2+1)). [Colin Barker, Mar 07 2013]

Crossrefs

Cf. A105842 (associated m).

Sequence in context: A183627 A184544 A251345 * A127456 A114484 A014369

Adjacent sequences: A105838 A105839 A105840 * A105842 A105843 A105844

Keyword

nonn,easy

Author

Pierre CAMI, Apr 22 2005

Extensions

a(10)-a(15) from Colin Barker, Mar 07 2013

Status

approved