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A041443 Denominators of continued fraction convergents to sqrt(237). 2
1, 2, 3, 5, 38, 385, 2733, 3118, 5851, 14820, 450451, 915722, 1366173, 2281895, 17339438, 175676275, 1247073363, 1422749638, 2669823001, 6762395640, 205541692201, 417845780042, 623387472243, 1041233252285, 7912020238238, 80161435634665, 569042069680893 (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, 0, 0, 456302, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

FORMULA

G.f.: -(x^18 -2*x^17 +3*x^16 -5*x^15 +38*x^14 -385*x^13 +2733*x^12 -3118*x^11 +5851*x^10 -14820*x^9 -5851*x^8 -3118*x^7 -2733*x^6 -385*x^5 -38*x^4 -5*x^3 -3*x^2 -2*x -1) / (x^20 -456302*x^10 +1). - Colin Barker, Nov 17 2013

a(n) = 456302*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 18 2013

MATHEMATICA

Denominator[Convergents[Sqrt[237], 30]] (* Vincenzo Librandi, Dec 18 2013 *)

PROG

(MAGMA) I:=[1, 2, 3, 5, 38, 385, 2733, 3118, 5851, 14820, 450451, 915722, 1366173, 2281895, 17339438, 175676275, 1247073363, 1422749638, 2669823001, 6762395640]; [n le 20 select I[n] else 456302*Self(n-10)-Self(n-20): n in [1..30]]; // Vincenzo Librandi, Dec 18 2013

CROSSREFS

Cf. A041442, A040221.

Sequence in context: A089213 A029499 A128026 * A057775 A215321 A215309

Adjacent sequences:  A041440 A041441 A041442 * A041444 A041445 A041446

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 17 2013

STATUS

approved

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Last modified June 24 04:38 EDT 2019. Contains 324318 sequences. (Running on oeis4.)