A105839 Numbers n such that n^2 = 19*m^2 + 19*m + 1.

1, 37, 2927, 68171, 183769, 4280053, 338355383, 7880431259, 21243328861, 494765566657, 39113205561107, 910962092609711, 2455686329490109, 57193909970135833, 4521408336114491603, 105305395973616940919, 283872428295154291321, 6611501604232996456477

Offset

1,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,115598,0,0,0,-1).

Formula

Define a(1)=0, a(2)=39, a(3)=2927, a(4)=68171, a(5)=115598*a(1)+a(4), a(6)=115598*a(2)+a(3), a(7)=115598*a(3)+a(2), a(8)=115598*a(4)+a(1) then a(n)=115598*a(n-4)-a(n-8).

G.f.: x*(x+1)*(x^6+36*x^5+2891*x^4+65280*x^3+2891*x^2+36*x+1) / ((x^4-340*x^2+1)*(x^4+340*x^2+1)). - Colin Barker, Mar 06 2013

Crossrefs

Cf. A101180 (associated m).

Sequence in context: A295530 A174750 A183524 * A141087 A218822 A220385

Adjacent sequences: A105836 A105837 A105838 * A105840 A105841 A105842

Keyword

nonn,easy

Author

Pierre CAMI, Apr 22 2005

Extensions

a(13)-a(18) from Colin Barker, Mar 06 2013

Status

approved