OFFSET
0,1
COMMENTS
a(n+1)/a(n) converges to (322 + sqrt(103680))/2 = 321.996894379... a(0)/a(1) = 2/322; a(1)/a(2) = 322/103682; a(2)/a(3) = 103682/33385282; a(3)/a(4) = 33385282/10749957122; etc. Lim_{n -> inf} a(n)/a(n+1) = 0.00310562... = 2/(322 + sqrt(103680)) = (322 - sqrt(103680))/2.
LINKS
Nathaniel Johnston, Table of n, a(n) for n = 0..100
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (322, -1).
FORMULA
a(n) = 322*a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 322
a(n) = ((322 + sqrt(103680))/2)^n + ((322 - sqrt(103680))/2)^n.
(a(n))^2 = a(2n) + 2.
G.f.: (2-322*x)/(1-322*x+x^2). - Philippe Deléham, Nov 02 2008
EXAMPLE
a(4) = 10749957122 = 322*a(3) - a(2) = 322*33385282 - 103682 = ((322 + sqrt(103680))/2)^4 + ((322 - sqrt(103680))/2)^4.
MATHEMATICA
Table[LucasL[12n], {n, 0, 13}] (* Indranil Ghosh, Mar 15 2017 *)
PROG
(Magma) [ Lucas(12*n) : n in [0..70]]; // Vincenzo Librandi, Apr 15 2011
(PARI) Vec((2 - 322*x)/(1 - 322*x + x^2) + O(x^14)) \\ Indranil Ghosh, Mar 15 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Jan 09 2004
EXTENSIONS
a(11) - a(13) from Vincenzo Librandi, Apr 15 2011
STATUS
approved