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A042882 Numerators of continued fraction convergents to sqrt(973). 2
31, 156, 811, 1778, 15035, 31848, 174275, 903223, 56174101, 281773728, 1465042741, 3211859210, 27159916421, 57531692052, 314818376681, 1631623575457, 101475480055015, 509009023850532, 2646520599307675, 5802050222465882, 49062922379034731, 103927894980535344 (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, 0, 0, 0, 0, 1806446, 0, 0, 0, 0, 0, 0, 0, -1).

FORMULA

G.f.: (31 +156*x +811*x^2 +1778*x^3 +15035*x^4 +31848*x^5 +174275*x^6 +903223*x^7 +174275*x^8 -31848*x^9 +15035*x^10 -1778*x^11 +811*x^12 -156*x^13 +31*x^14 -x^15)/(1 -1806446*x^8 +x^16). - Vincenzo Librandi, Dec 08 2013

a(n) = 1806446*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 08 2013

MATHEMATICA

Numerator[Convergents[Sqrt[973], 30]] (* or *) CoefficientList[Series[(31 + 156 x + 811 x^2 + 1778 x^3 + 15035 x^4 + 31848 x^5 + 174275 x^6 + 903223 x^7 + 174275 x^8 - 31848 x^9 + 15035 x^10 - 1778 x^11 + 811 x^12 - 156 x^13 + 31 x^14 - x^15)/(1 - 1806446 x^8 + x^16), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 08 2013 *)

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1806446, 0, 0, 0, 0, 0, 0, 0, -1}, {31, 156, 811, 1778, 15035, 31848, 174275, 903223, 56174101, 281773728, 1465042741, 3211859210, 27159916421, 57531692052, 314818376681, 1631623575457}, 40] (* Harvey P. Dale, Jul 04 2017 *)

PROG

(MAGMA) I:=[31, 156, 811, 1778, 15035, 31848, 174275, 903223, 56174101, 281773728, 1465042741, 3211859210, 27159916421, 57531692052, 314818376681, 1631623575457]; [n le 16 select I[n] else 1806446*Self(n-8)-Self(n-16): n in [1..30]]; // Vincenzo Librandi, Dec 08 2013

CROSSREFS

Cf. A042883.

Sequence in context: A176922 A134553 A042880 * A045160 A142906 A157373

Adjacent sequences:  A042879 A042880 A042881 * A042883 A042884 A042885

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Vincenzo Librandi, Dec 08 2013

STATUS

approved

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Last modified March 21 10:00 EDT 2019. Contains 321368 sequences. (Running on oeis4.)