A105842 - OEIS

%I #11 Jun 13 2015 00:51:47

%S 0,55,9064,1480479,3140319,512899624,83770465015,13681996386240,

%T 29021570410560,4740012143979895,774172961946305704,

%U 126443510439085951839,268205687063091955359,43805286749779801393384,7154595296776971135630775,1168540093186822172351633280

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

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,9241598,-9241598,0,0,-1,1).

%F 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).

%F 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]

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

%K nonn,easy

%O 1,2

%A _Pierre CAMI_, Apr 22 2005

%E a(10)-a(16) from _Colin Barker_, Mar 07 2013