A105844 Numbers n such that 37*n^2 + 37*n + 1 is a square.

0, 24, 48, 3576, 7080, 522144, 1033704, 76229520, 150913776, 11128987848, 22032377664, 1624755996360, 3216576225240, 237203246480784, 469598096507448, 34630049230198176, 68558105513862240, 5055749984362452984

Offset

1,2

Links

Table of n, a(n) for n=1..18.

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

Formula

Define a(1)=0, a(2)=24, a(3)=146*a(1)+72-a(2), a(4)=146*a(2)+72-a(1), then a(n) = 146*a(n-2)+72-a(n-4).

G.f.: -24*x^2*(x^2+x+1)/(x^5-x^4-146*x^3+146*x^2+x-1). [Harvey P. Dale, Mar 14 2011]

Mathematica

CoefficientList[Series[-((24x(x^2+x+1))/(x^5-x^4-146x^3 +146x^2+x-1)), {x, 0, 30}], x]  (* Harvey P. Dale, Mar 14 2011 *)

Crossrefs

Cf. A105843 (square roots of 37*a(n)^2+37*a(n)+1).

Sequence in context: A268486 A288460 A352699 * A129837 A042140 A042138

Adjacent sequences: A105841 A105842 A105843 * A105845 A105846 A105847

Keyword

nonn,easy

Author

Pierre CAMI, Apr 22 2005

Extensions

More terms from Harvey P. Dale, Mar 14 2011

Status

approved