login
A101180
Numbers n such that 19*n^2 + 19*n + 1 is a square.
3
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
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
CROSSREFS
Cf. A105839.
Sequence in context: A099126 A172919 A286394 * A128875 A199801 A278857
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