A042240 Numerators of continued fraction convergents to sqrt(646).

25, 51, 127, 305, 15377, 31059, 77495, 186049, 9379945, 18945939, 47271823, 113489585, 5721751073, 11556991731, 28835734535, 69228460801, 3490258774585, 7049746009971, 17589750794527

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,0,610,0,0,0,-1).

Formula

G.f.: (1 +x)*(25 +26*x +101*x^2 +204*x^3 -77*x^4 +26*x^5 -x^6)/(1 -610*x^4 +x^8) = (25 +51*x +127*x^2 +305*x^3 +127*x^4 -51*x^5 +25*x^6 -x^7)/(1 -610*x^4 +x^8). - Vincenzo Librandi, Nov 19 2013

a(n) = 610*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 19 2013

Mathematica

Numerator[Convergents[Sqrt[646], 30]] (* or *) CoefficientList[Series[(25 + 51 x + 127 x^2 + 305 x^3 + 127 x^4 - 51 x^5 + 25 x^6 - x^7)/(1 - 610 x^4 + x^8), {x, 0, 20}], x] (* Vincenzo Librandi, Nov 19 2013 *)

Prog

(Magma) I:=[25, 51, 127, 305, 15377, 31059, 77495, 186049]; [n le 8 select I[n] else 610*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 19 2013

Crossrefs

Cf. A042241.

Sequence in context: A338079 A337630 A270693 * A042242 A042244 A042246

Adjacent sequences: A042237 A042238 A042239 * A042241 A042242 A042243

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved