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A041107 Denominators of continued fraction convergents to sqrt(61). 2
1, 1, 5, 16, 21, 58, 137, 195, 722, 3083, 3805, 56353, 60158, 296985, 951113, 1248098, 3447309, 8142716, 11590025, 42912791, 183241189, 226153980, 3349396909, 3575550889, 17651600465, 56530352284, 74181952749, 204894257782, 483970468313, 688864726095 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,59436,0,0,0,0,0,0,0,0,0,0,1).

FORMULA

G.f.: -(x^20 -x^19 +5*x^18 -16*x^17 +21*x^16 -58*x^15 +137*x^14 -195*x^13 +722*x^12 -3083*x^11 +3805*x^10 +3083*x^9 +722*x^8 +195*x^7 +137*x^6 +58*x^5 +21*x^4 +16*x^3 +5*x^2 +x +1) / (x^22 +59436*x^11 -1). - Colin Barker, Nov 12 2013

a(n) = 59436*a(n-11) + a(n-22). - Vincenzo Librandi, Dec 11 2013

MATHEMATICA

Denominator[Convergents[Sqrt[61], 30]] (* Vincenzo Librandi, Dec 11 2013 *)

PROG

(MAGMA) I:=[1, 1, 5, 16, 21, 58, 137, 195, 722, 3083, 3805, 56353, 60158, 296985, 951113, 1248098, 3447309, 8142716, 11590025, 42912791, 183241189, 226153980]; [n le 22 select I[n] else 59436*Self(n-11)+Self(n-22): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013

CROSSREFS

Cf. A041106, A010145, A020818, A010514.

Sequence in context: A022140 A041855 A030691 * A042603 A031120 A029450

Adjacent sequences:  A041104 A041105 A041106 * A041108 A041109 A041110

KEYWORD

nonn,cofr,easy,frac

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 12 2013

STATUS

approved

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Last modified October 15 23:54 EDT 2019. Contains 328038 sequences. (Running on oeis4.)