A101180 Numbers n such that 19*n^2 + 19*n + 1 is a square.

0, 8, 671, 15639, 42159, 981911, 77624048, 1807894920, 4873553880, 113507005568, 8973184757831, 208989037004319, 563373081435879, 13121182828725551, 1037282211558181688, 24158714697817430640, 65124801462951244560, 1516782492521509296728

Offset

1,2

Comments

Define a(1)=0, a(2)=8, a(3)=671, a(4)=15639, a(5)=42159, a(6)=981911, the first 6 terms found for the sequence then a(7)=57799*(2*a(3)+1)-a(2)-1, a(8)=57799*(2*a(4)+1)-a(1)-1 for n>8 a(n)=57799*(2*a(n-4)+1)-a(n-8)-1 remark:57799 = 38*39*39+1 =2*19*(39^2)+1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..790

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

Formula

G.f.: -x^2*(8*x^6+663*x^5+14968*x^4+26520*x^3+14968*x^2+663*x+8) / ((x-1)*(x^4-340*x^2+1)*(x^4+340*x^2+1)). - Colin Barker, Mar 05 2013

Mathematica

CoefficientList[Series[-x^2(8x^6+663x^5+14968x^4+26520x^3+14968x^2+663x+8)/((x-1)(x^4-340x^2+1)(x^4+340x^2+1)), {x, 0, 30}], x] (* or *) LinearRecurrence[{1, 0, 0, 115598, -115598, 0, 0, -1, 1}, {0, 0, 8, 671, 15639, 42159, 981911, 77624048, 1807894920}, 30] (* Harvey P. Dale, Aug 16 2025 *)

Crossrefs

Cf. A105839.

Sequence in context: A099126 A172919 A286394 * A128875 A199801 A278857

Adjacent sequences: A101177 A101178 A101179 * A101181 A101182 A101183

Keyword

nonn,easy

Author

Pierre CAMI, Apr 06 2005, Apr 22 2005

Extensions

Edited by N. J. A. Sloane, Aug 29 2008 at the suggestion of R. J. Mathar

More terms (using recursive formula in comment) from Jon E. Schoenfield, Jul 10 2010

a(18) from Colin Barker, Mar 05 2013

Status

approved