login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A239364 Numbers n such that (n^2-4)/10 is a square. 2
38, 1442, 54758, 2079362, 78960998, 2998438562, 113861704358, 4323746327042, 164188498723238, 6234839205156002, 236759701297204838, 8990633810088627842, 341407325082070653158, 12964487719308596192162, 492309126008644584648998, 18694782300609185620469762 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Values of x satisfying the Pellian equation x^2 - 10*y^2 = 4.

LINKS

Colin Barker, Table of n, a(n) for n = 1..600

Index entries for linear recurrences with constant coefficients, signature (38,-1).

FORMULA

a(n) = 2*A078986(n).

a(n) = (19+6*sqrt(10))^(-n)+(19+6*sqrt(10))^n.

a(n) = 38*a(n-1)-a(n-2).

G.f.: -2*x*(x-19) / (x^2-38*x+1).

EXAMPLE

1442 is in the sequence because (1442^2-4)/10 = 207936 = 456^2.

MATHEMATICA

LinearRecurrence[{38, -1}, {38, 1442}, 30] (* Harvey P. Dale, Dec 19 2014 *)

PROG

(PARI) Vec(-2*x*(x-19)/(x^2-38*x+1) + O(x^100))

CROSSREFS

Cf. A078986, A239365.

Sequence in context: A170757 A218740 A158702 * A078987 A009982 A041685

Adjacent sequences:  A239361 A239362 A239363 * A239365 A239366 A239367

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Mar 17 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 12 07:00 EST 2019. Contains 329052 sequences. (Running on oeis4.)