A105842 Numbers n such that 31*n^2 + 31*n + 1 is a square.

0, 55, 9064, 1480479, 3140319, 512899624, 83770465015, 13681996386240, 29021570410560, 4740012143979895, 774172961946305704, 126443510439085951839, 268205687063091955359, 43805286749779801393384, 7154595296776971135630775, 1168540093186822172351633280

Offset

1,2

Links

Table of n, a(n) for n=1..16.

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

Formula

a(1)=0, a(2)=55, a(3)=9064, a(4)=1480479, a(5)=9241598*a(1)+4620798-a(4), a(6)=9241598*a(2)+4620798-a(3), a(7)=9241598*a(3)+4620798-a(2), a(8)=9241598*a(4)+4620798-a(1), then a(n)=9241598*a(n-4)+4620798-a(n-8).

G.f.: -x^2*(55*x^6+9009*x^5+1471415*x^4+1659840*x^3+1471415*x^2+9009*x+55) / ((x-1)*(x^4-3040*x^2+1)*(x^4+3040*x^2+1)). [Colin Barker, Mar 07 2013]

Crossrefs

Cf. A105841 (square roots of 31*a(n)^2+31*a(n)+1).

Sequence in context: A269500 A090813 A145617 * A113632 A202161 A221734

Adjacent sequences: A105839 A105840 A105841 * A105843 A105844 A105845

Keyword

nonn,easy

Author

Pierre CAMI, Apr 22 2005

Extensions

a(10)-a(16) from Colin Barker, Mar 07 2013

Status

approved