A042244 Numerators of continued fraction convergents to sqrt(648).

25, 51, 280, 1731, 8935, 19601, 988985, 1997571, 10976840, 67858611, 350269895, 768398401, 38770189945, 78308778291, 430314081400, 2660193266691, 13731280414855, 30122754096401, 1519868985234905

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,39202,0,0,0,0,0,-1).

Formula

G.f.: (25 + 51*x + 280*x^2 + 1731*x^3 + 8935*x^4 + 19601*x^5 + 8935*x^6 - 1731*x^7 + 280*x^8 - 51*x^9 + 25*x^10 - x^11)/(1 - 39202*x^6 + x^12). - Vincenzo Librandi, Nov 19 2013

a(n) = 39202*a(n-6) - a(n-12). - Vincenzo Librandi, Nov 19 2013

Mathematica

Numerator[Convergents[Sqrt[648], 30]] (* or *) CoefficientList[Series[(25 + 51 x + 280 x^2 + 1731 x^3 + 8935 x^4 + 19601 x^5 + 8935 x^6 - 1731 x^7 + 280 x^8 - 51 x^9 + 25 x^10 - x^11)/(1 - 39202 x^6 + x^12), {x, 0, 20}], x] (* Vincenzo Librandi, Nov 19 2013 *)

Prog

(Magma) I:=[25, 51, 280, 1731, 8935, 19601, 988985, 1997571, 10976840, 67858611, 350269895, 768398401]; [n le 12 select I[n] else 39202*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Nov 19 2013

Crossrefs

Cf. A042245.

Sequence in context: A270693 A042240 A042242 * A042246 A042248 A132766

Adjacent sequences: A042241 A042242 A042243 * A042245 A042246 A042247

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved