login
A042748
Numerators of continued fraction convergents to sqrt(905).
2
30, 361, 21690, 260641, 15660150, 188182441, 11306606610, 135867461761, 8163354312270, 98096119209001, 5893930506852330, 70825262201436961, 4255409662593069990, 51135741213318276841, 3072399882461689680450
OFFSET
0,1
FORMULA
G.f.: (30 +361*x +30*x^2 -x^3)/(1 -722*x^2 +x^4). - Vincenzo Librandi, Dec 03 2013
a(n) = 722*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 03 2013
MATHEMATICA
Numerator[Convergents[Sqrt[905], 30]] (* or *) CoefficientList[Series[(30 + 361 x + 30 x^2 - x^3)/(1 - 722 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 03 2013 *)
LinearRecurrence[{0, 722, 0, -1}, {30, 361, 21690, 260641}, 20] (* Harvey P. Dale, Mar 05 2022 *)
PROG
(Magma) I:=[30, 361, 21690, 260641]; [n le 4 select I[n] else 722*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 03 2013
CROSSREFS
Cf. A042749.
Sequence in context: A086864 A138441 A058837 * A202074 A251895 A022690
KEYWORD
nonn,cofr,frac,easy
AUTHOR
STATUS
approved