OFFSET
0,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..100
Index entries for linear recurrences with constant coefficients, signature (340,-1).
FORMULA
a(n+2) = 340*a(n+1) - a(n).
a(n+1) = 170*a(n) + 39*sqrt(19*(w(n))^2 + 81).
G.f.: (220 + x)/(1 - 340*x + x^2).
a(n) = ((959*sqrt(19) + 4180)/38)*(170 + 39*sqrt(19))^n + ((-959*sqrt(19) + 4180)/38)*(170 - 39*sqrt(19))^n.
MAPLE
w(0):=220:for n from 0 to 20 do w(n+1):=170*w(n)+39*sqrt(19*(w(n))^2+81) :od: seq(w(n), n=0..20); for n from 0 to 20 do u(n):=simplify((959*sqrt(19)+4180)/38*(170+39*sqrt(19))^(n)+(-959*sqrt(19)+4180)/38*(170-39*sqrt(19))^(n)):od:seq(u(n), n=0..20); taylor(((220+74801*z-220*340*z)/(1-340*z+z^2)), z=0, 21);
MATHEMATICA
LinearRecurrence[{340, -1}, {220, 74801}, 50] (* G. C. Greubel, Jun 27 2016 *)
RecurrenceTable[{a[1] == 220, a[2] == 74801, a[n] == 340 a[n-1] - a[n-2]}, a, {n, 15}] (* Vincenzo Librandi, Jun 28 2016 *)
PROG
(Magma) I:=[220, 74801]; [n le 2 select I[n] else 340*Self(n-1)-Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jun 28 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Richard Choulet, Nov 13 2009
STATUS
approved