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A042240 Numerators of continued fraction convergents to sqrt(646). 2
25, 51, 127, 305, 15377, 31059, 77495, 186049, 9379945, 18945939, 47271823, 113489585, 5721751073, 11556991731, 28835734535, 69228460801, 3490258774585, 7049746009971, 17589750794527 (list; graph; refs; listen; history; text; internal format)
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: A042232 A273868 A270693 * A042242 A042244 A042246

Adjacent sequences:  A042237 A042238 A042239 * A042241 A042242 A042243

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified October 20 12:34 EDT 2018. Contains 316379 sequences. (Running on oeis4.)