%I #30 Sep 08 2022 08:46:12

%S 1,63,3905,242047,15003009,929944511,57641556673,3572846569215,

%T 221458845734657,13726875588979519,850844827670995521,

%U 52738652440012742783,3268945606453119057025,202621888947653368792767,12559288169148055746094529,778473244598231802889068031

%N a(n) = A041105(4n+1).

%H Colin Barker, <a href="/A258684/b258684.txt">Table of n, a(n) for n = 0..557</a>

%H E. Kilic, Y. T. Ulutas, N. Omur, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Omur/omur6.html">A Formula for the Generating Functions of Powers of Horadam's Sequence with Two Additional Parameters</a>, J. Int. Seq. 14 (2011) #11.5.6, table 4, k=1, t=4

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (62,-1).

%F a(n) = (1/2-2/sqrt(15))*(31-8*sqrt(15))^n+((15+4*sqrt(15))*(31+8*sqrt(15))^n)/30.

%F a(n) = 62*a(n-1)-a(n-2). - _Colin Barker_, Jun 07 2015

%F G.f.: (x+1) / (x^2-62*x+1). - _Colin Barker_, Jun 07 2015

%t a[c_, p_, n_] := Module[{},

%t l := Length[ContinuedFraction[ Sqrt[ c]][[2]]];

%t d := Denominator[Convergents[Sqrt[c], n l]] ;

%t t := Table[d[[i + 1]], {i, p, Length[d] - 1, l}] ;

%t Return[t];

%t ];

%t a[60, 1, 20]

%t CoefficientList[Series[(1 + x)/(x^2 - 62 x + 1), {x, 0, 40}], x] (* _Vincenzo Librandi_, Jun 08 2015 *)

%t LinearRecurrence[{62,-1},{1,63},30] (* _Harvey P. Dale_, Dec 24 2015 *)

%o (PARI) Vec((x+1)/(x^2-62*x+1) + O(x^100)) \\ _Colin Barker_, Jun 07 2015

%o (Magma) I:=[1,63]; [n le 2 select I[n] else 62*Self(n-1)-Self(n-2): n in [1..45]]; // _Vincenzo Librandi_, Jun 08 2015

%Y Cf. A041105 (denominators of continued fraction convergents to sqrt(60)).

%K nonn,easy,frac

%O 0,2

%A _Gerry Martens_, Jun 07 2015