A042278 - OEIS

%I #19 Jul 04 2021 14:51:51

%S 25,26,103,129,361,851,2063,2914,10805,13719,696755,710474,2828177,

%T 3538651,9905479,23349609,56604697,79954306,296467615,376421921,

%U 19117563665,19493985586,77599520423,97093506009,271786532441,640666570891,1553119674223,2193786245114

%N Numerators of continued fraction convergents to sqrt(665).

%H Vincenzo Librandi, <a href="/A042278/b042278.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 27438, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

%F G.f.: -(x^19 -25*x^18 +26*x^17 -103*x^16 +129*x^15 -361*x^14 +851*x^13 -2063*x^12 +2914*x^11 -10805*x^10 -13719*x^9 -10805*x^8 -2914*x^7 -2063*x^6 -851*x^5 -361*x^4 -129*x^3 -103*x^2 -26*x -25) / (x^20 -27438*x^10 +1). - _Colin Barker_, Dec 06 2013

%p convert(sqrt(665),confrac,30,cvgts): numer(cvgts); # _Wesley Ivan Hurt_, Dec 07 2013

%t Numerator[Convergents[Sqrt[665], 30]] (* _Vincenzo Librandi_, Nov 20 2013 *)

%t LinearRecurrence[{0,0,0,0,0,0,0,0,0,27438,0,0,0,0,0,0,0,0,0,-1},{25,26,103,129,361,851,2063,2914,10805,13719,696755,710474,2828177,3538651,9905479,23349609,56604697,79954306,296467615,376421921},30] (* _Harvey P. Dale_, Jul 04 2021 *)

%Y Cf. A042279, A040639.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Dec 06 2013