login
A041256
Numerators of continued fraction convergents to sqrt(140).
2
11, 12, 59, 71, 1621, 1692, 8389, 10081, 230171, 240252, 1191179, 1431431, 32682661, 34114092, 169139029, 203253121, 4640707691, 4843960812, 24016550939, 28860511751, 658947809461, 687808321212
OFFSET
0,1
FORMULA
G.f.: (11 +12*x +59*x^2 +71x^3 +59x^4 -12x^5 +11x^6 -x^7) / ((1 -12*x^2 +x^4)*(1 +12*x^2 +x^4)). - Vincenzo Librandi, Nov 01 2013
a(n) = 142*a(n-4)-a(n-8). - Vincenzo Librandi, Nov 01 2013
MATHEMATICA
Numerator[Convergents[Sqrt[140], 30]] (* or *) CoefficientList[Series[(11 + 12 x + 59 x^2 + 71 x^3 + 59 x^4 - 12 x^5 + 11 x^6 - x^7)/(1 - 142 x^4 + x^8), {x, 0, 25}], x] (* Vincenzo Librandi, Oct 31 2013 *)
LinearRecurrence[{0, 0, 0, 142, 0, 0, 0, -1}, {11, 12, 59, 71, 1621, 1692, 8389, 10081}, 30] (* Harvey P. Dale, Feb 23 2015 *)
PROG
(Magma) I:=[11, 12, 59, 71, 1621, 1692, 8389, 10081]; [n le 8 select I[n] else 142*Self(n-4)-Self(n-8): n in [1..25]]; // Vincenzo Librandi, Nov 01 2013
CROSSREFS
Cf. A041257.
Sequence in context: A248323 A291059 A041254 * A059181 A041258 A082262
KEYWORD
nonn,cofr,frac,easy
AUTHOR
STATUS
approved