login
A042062
Numerators of continued fraction convergents to sqrt(555).
2
23, 24, 47, 165, 212, 801, 1013, 1814, 84457, 86271, 170728, 598455, 769183, 2906004, 3675187, 6581191, 306409973, 312991164, 619401137, 2171194575, 2790595712, 10542981711, 13333577423, 23876559134
OFFSET
0,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 3628, 0, 0, 0, 0, 0, 0, 0, -1).
FORMULA
G.f.: (23 +24*x +47*x^2 +165*x^3 +212*x^4 +801*x^5 +1013*x^6 +1814*x^7 +1013*x^8 -801*x^9 +212*x^10 -165*x^11 +47*x^12 -24*x^13 +23*x^14 -x^15)/(1 -3628*x^8 +x^16). - Vincenzo Librandi, Nov 13 2013
a(n) = 3628*a(n-8) - a(n-16). - Vincenzo Librandi, Nov 14 2013
MATHEMATICA
Numerator[Convergents[Sqrt[555], 30]] (* or *) CoefficientList[Series[(23 + 24 x + 47 x^2 + 165 x^3 + 212 x^4 + 801 x^5 + 1013 x^6 + 1814 x^7 + 1013 x^8 - 801 x^9 + 212 x^10 - 165 x^11 + 47 x^12 - 24 x^13 + 23 x^14 - x^15)/(1 - 3628 x^8 + x^16), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 14 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 3628, 0, 0, 0, 0, 0, 0, 0, -1}, {23, 24, 47, 165, 212, 801, 1013, 1814, 84457, 86271, 170728, 598455, 769183, 2906004, 3675187, 6581191}, 30] (* Harvey P. Dale, Dec 28 2015 *)
PROG
(Magma) I:=[23, 24, 47, 165, 212, 801, 1013, 1814, 84457, 86271, 170728, 598455, 769183, 2906004, 3675187, 6581191]; [n le 16 select I[n] else 3628*Self(n-8)-Self(n-16): n in [1..30]]; // Vincenzo Librandi, Nov 14 2013
CROSSREFS
Cf. A042063.
Sequence in context: A042070 A042072 A042064 * A042060 A042058 A045859
KEYWORD
nonn,cofr,frac,easy,less
AUTHOR
STATUS
approved