A106176 Numbers n such that 67*n^2 + 67*n + 1 is a square.

0, 16, 1440, 389295, 33994015, 1802660535, 2968421391, 157411709575, 13745486642391, 3714721448623416, 324376465956415720, 17201282202880383816, 28325163305411682840, 1502048325307681783960, 131161685794667995415400, 35446480734732882983897895

Offset

1,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,9542163854,-9542163854,0,0,0,0,-1,1).

Formula

a(1)=0, a(2)=16, a(3)=1440, a(4)=389295, a(5)=33994015, a(6)=1802660535, a(7)=9542163854*a(1)+4771081926-a(6), a(8)=9542163854*a(2)+4771081926-a(5), a(9)=9542163854*a(3)+4771081926-a(4), a(10)=9542163854*a(4)+4771081926-a(3), a(11)=9542163854*a(5)+4771081926-a(2), a(12)=9542163854*a(6)+4771081926-a(1), then a(n)=9542163854*a(n-6)+4771081926-a(n-12).

G.f.: -x^2*(16*x^10 +1424*x^9 +387855*x^8 +33604720*x^7 +1768666520*x^6 +1165760856*x^5 +1768666520*x^4 +33604720*x^3 +387855*x^2 +1424*x +16) / ((x -1)*(x^6 -97684*x^3 +1)*(x^6 +97684*x^3 +1)). [Colin Barker, Mar 07 2013]

Mathematica

CoefficientList[Series[-x^2(16x^10+1424x^9+387855x^8+33604720x^7+1768666520x^6+1165760856x^5+1768666520x^4+33604720x^3+387855x^2+1424x+16)/((x-1)(x^6-97684x^3+1)(x^6+97684x^3+1)), {x, 0, 30}], x] (* or *) LinearRecurrence[{1, 0, 0, 0, 0, 9542163854, -9542163854, 0, 0, 0, 0, -1, 1}, {0, 0, 16, 1440, 389295, 33994015, 1802660535, 2968421391, 157411709575, 13745486642391, 3714721448623416, 324376465956415720, 17201282202880383816}, 30] (* Harvey P. Dale, Aug 03 2021 *)

Crossrefs

Cf. A106175 (square roots of 67*a(n)^2+67*a(n)+1).

Sequence in context: A351760 A330335 A160251 * A263975 A193128 A223101

Adjacent sequences: A106173 A106174 A106175 * A106177 A106178 A106179

Keyword

nonn,easy

Author

Pierre CAMI, Apr 24 2005

Extensions

a(15)-a(16) from Colin Barker, Mar 07 2013

Status

approved