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A041195 Denominators of continued fraction convergents to sqrt(108). 2
1, 2, 3, 5, 23, 28, 51, 130, 2651, 5432, 8083, 13515, 62143, 75658, 137801, 351260, 7163001, 14677262, 21840263, 36517525, 167910363, 204427888, 372338251, 949104390, 19354426051, 39657956492, 59012382543, 98670339035, 453693738683, 552364077718 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,2702,0,0,0,0,0,0,0,-1).

FORMULA

G.f.: -(x^14 -2*x^13 +3*x^12 -5*x^11 +23*x^10 -28*x^9 +51*x^8 -130*x^7 -51*x^6 -28*x^5 -23*x^4 -5*x^3 -3*x^2 -2*x -1) / ((x^8 -52*x^4 +1)*(x^8 +52*x^4 +1)). - Colin Barker, Nov 14 2013

a(n) = 2702*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 12 2013

MATHEMATICA

Denominator[Convergents[Sqrt[108], 30]] (* Vincenzo Librandi, Dec 12 2013 *)

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 2702, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 2, 3, 5, 23, 28, 51, 130, 2651, 5432, 8083, 13515, 62143, 75658, 137801, 351260}, 30] (* Harvey P. Dale, Jan 08 2016 *)

PROG

(MAGMA) I:=[1, 2, 3, 5, 23, 28, 51, 130, 2651, 5432, 8083, 13515, 62143, 75658, 137801, 351260]; [n le 16 select I[n] else 2702*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 12 2013

CROSSREFS

Cf. A041194, A010174.

Sequence in context: A024782 A024775 A024767 * A042141 A122004 A023231

Adjacent sequences:  A041192 A041193 A041194 * A041196 A041197 A041198

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 14 2013

STATUS

approved

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Last modified May 21 14:16 EDT 2022. Contains 353909 sequences. (Running on oeis4.)