A042244 - OEIS

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

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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