A042910 Numerators of continued fraction convergents to sqrt(987).

31, 63, 157, 377, 23531, 47439, 118409, 284257, 17742343, 35768943, 89280229, 214329401, 13377703091, 26969735583, 67317174257, 161604084097, 10086770388271, 20335144860639, 50757060109549, 121849265079737, 7605411495053243, 15332672255186223, 38270756005425689

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, 754, 0, 0, 0, -1).

Formula

G.f.: (31 +63*x +157*x^2 +377*x^3 +157*x^4 -63*x^5 +31*x^6 -x^7)/(1 -754*x^4 +x^8). - Vincenzo Librandi, Dec 09 2013

a(n) = 754*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 09 2013

Mathematica

Numerator[Convergents[Sqrt[987], 20]] (* Harvey P. Dale, Mar 15 2013 *)
CoefficientList[Series[(31 + 63 x + 157 x^2 + 377 x^3 + 157 x^4 - 63 x^5 + 31 x^6 - x^7)/(1 - 754 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 09 2013 *)

Prog

(Magma) I:=[31, 63, 157, 377, 23531, 47439, 118409, 284257]; [n le 8 select I[n] else 754*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Dec 09 2013

Crossrefs

Cf. A042911.

Sequence in context: A042902 A042900 A239128 * A042908 A042912 A167783

Adjacent sequences: A042907 A042908 A042909 * A042911 A042912 A042913

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Dec 09 2013

Status

approved