OFFSET
0,1
COMMENTS
Numbers n such that ((n^2 + 1)/10) is a square. - Vincenzo Librandi, Jan 02 2012
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (38,-1).
FORMULA
a(n) = (1/2)*((-3+sqrt(10))*(19+6*sqrt(10))^n + (-3-sqrt(10))*(19-6*sqrt(10))^n).
a(n) = -a(-n+1).
G.f.: -3*(1-39*x)/(1-38*x+x^2). - Bruno Berselli, Jan 03 2011
E.g.f.: exp(19*x)*(-3*cosh(6*sqrt(10)*x) + sqrt(10)*sinh(6*sqrt(10)*x)). - Stefano Spezia, Apr 24 2025
MATHEMATICA
LinearRecurrence[{38, -1}, {-3, 3}, 30] (* Harvey P. Dale, Jan 14 2015 *)
PROG
(Magma) [-3] cat [n: n in [0..10^7]|IsSquare((n^2+1)/10)]; // Vincenzo Librandi, Jan 02 2012
(Python)
from itertools import islice
def A173127_gen(): # generator of terms
x, y = -30, 10
while True:
yield x//10
x, y = x*19+y*60, x*6+y*19
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Artur Jasinski, Feb 10 2010
STATUS
approved