%I #18 Jun 26 2022 23:36:34

%S 31,32,63,95,158,885,5468,6353,37233,80819,441328,522147,3574210,

%T 18393197,21967407,40360604,62328011,102688615,6429022141,6531710756,

%U 12960732897,19492443653,32453176550

%N Numerators of continued fraction convergents to sqrt(999).

%H Vincenzo Librandi, <a href="/A042934/b042934.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_36">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 205377230, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

%F a(n) = 205377230*a(n-18) - a(n-36). - _Wesley Ivan Hurt_, May 28 2021

%t Numerator[Convergents[Sqrt[999], 30]] (* _Vincenzo Librandi_, Dec 10 2013 *)

%o (PARI) A42934=contfracpnqn(c=contfrac(sqrt(999)), #c)[1,][^-1] \\ Discard possibly incorrect last element. NB: a(n) = A42934[n+1]! For more terms, use:

%o A042934(n)={n<#A42934 || A42934_upto(n+10); A42934[n+1]}

%o {A42934_upto(N,A=Vec(A42934,N))=for(n=#A42934+1,N, A[n]=205377230*A[n-18]-A[n-36]); A42934=A} \\ _M. F. Hasler_, Nov 01 2019

%Y Cf. A042935 (denominators).

%Y Analog for other sqrt(m): A001333 (m=2), A002531 (m=3), A001077 (m=5), A041006 (m=6), A041008 (m=7), A041010 (m=8), A005667 (m=10), A041014 (m=11), ..., A042936 (m=1000).

%K nonn,frac,easy

%O 0,1

%A _N. J. A. Sloane_