A041458 Numerators of continued fraction convergents to sqrt(245).

15, 16, 31, 47, 360, 2207, 15809, 18016, 33825, 51841, 1589055, 1640896, 3229951, 4870847, 37325880, 228826127, 1639108769, 1867934896, 3507043665, 5374978561, 164756400495, 170131379056, 334887779551, 505019158607, 3870021889800, 23725150497407

Offset

0,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,103682,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^19 -15*x^18 +16*x^17 -31*x^16 +47*x^15 -360*x^14 +2207*x^13 -15809*x^12 +18016*x^11 -33825*x^10 -51841*x^9 -33825*x^8 -18016*x^7 -15809*x^6 -2207*x^5 -360*x^4 -47*x^3 -31*x^2 -16*x -15) / ((x^10 -322*x^5 +1)*(x^10 +322*x^5 +1)). - Colin Barker, Nov 18 2013

a(n) = 103682*a(n-10)-a(n-20). - Wesley Ivan Hurt, May 07 2021

Mathematica

Convergents[Sqrt[245], 30]//Numerator (* or *) LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 103682, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {15, 16, 31, 47, 360, 2207, 15809, 18016, 33825, 51841, 1589055, 1640896, 3229951, 4870847, 37325880, 228826127, 1639108769, 1867934896, 3507043665, 5374978561}, 30] (* Harvey P. Dale, Jun 15 2023 *)

Crossrefs

Cf. A041459, A040229.

Sequence in context: A037971 A022105 A041456 * A041454 A041452 A041450

Adjacent sequences: A041455 A041456 A041457 * A041459 A041460 A041461

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 18 2013

Status

approved