OFFSET
0,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..100
Index entries for linear recurrences with constant coefficients, signature (0,74,0,-1).
FORMULA
G.f.: -(x^3-6*x^2-37*x-6) / (x^4-74*x^2+1). - Colin Barker, Nov 04 2013
From Gerry Martens, Jul 11 2015: (start)
Interspersion of 2 sequences [a0(n),a1(n)] for n>0:
a0(n) = (-3+sqrt(19/2))*(37+6*sqrt(38))^n-(6+sqrt(38))/(2*(37+6*sqrt(38))^n).
a1(n) = (1/(37+6*sqrt(38))^n+(37+6*sqrt(38))^n)/2. (End)
MATHEMATICA
Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[38], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 21 2011*)
Numerator[Convergents[Sqrt[38], 30]] (* Vincenzo Librandi, Oct 29 2013 *)
a0[n_] := (-3+Sqrt[19/2])*(37+6*Sqrt[38])^n-(6+Sqrt[38])/(2*(37+6*Sqrt[38])^n) // Simplify
a1[n_] := (1/(37+6*Sqrt[38])^n+(37+6*Sqrt[38])^n)/2 // FullSimplify
Flatten[MapIndexed[{a0[#], a1[#]}&, Range[20]]] (* Gerry Martens, Jul 11 2015 *)
LinearRecurrence[{0, 74, 0, -1}, {6, 37, 450, 2737}, 20] (* Harvey P. Dale, Oct 17 2020 *)
CROSSREFS
KEYWORD
nonn,cofr,frac,easy
AUTHOR
STATUS
approved