A105846 Numbers n such that 41*n^2 + 41*n + 1 is a square.

0, 704, 1344, 2887040, 5509760, 11831091264, 22578997184, 48483809114880, 92528724952320, 198686637921689024, 379182692275612224, 814217793719272507520, 1553890580416733943680, 3336664319974940814129984, 6367843219365083425590464, 13673649569039513737032168960

Offset

1,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (1,4098,-4098,-1,1).

Formula

Define a(1)=0, a(2)=704, a(3)=4098*a(1)+2048-a(2), a(4)=4098*a(2)+2048-a(1), then a(n)=4098*a(n-2)+2048-a(n-4).

G.f.: -64*x^2*(11*x^2+10*x+11) / ((x-1)*(x^2-64*x-1)*(x^2+64*x-1)). [Colin Barker, Mar 06 2013]

Crossrefs

Cf. A105845 (square roots of 41*a(n)^2+41*a(n)+1).

Sequence in context: A185571 A186923 A185807 * A323342 A237009 A185568

Adjacent sequences: A105843 A105844 A105845 * A105847 A105848 A105849

Keyword

nonn,easy

Author

Pierre CAMI, Apr 22 2005

Extensions

a(10)-a(16) from Colin Barker, Mar 06 2013

Status

approved