OFFSET
0,3
COMMENTS
The ratio a(n+1)/a(n) converges to 5 as n approaches infinity. - Felix P. Muga II, Mar 10 2014
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
F. P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, March 2014.
Index entries for linear recurrences with constant coefficients, signature (3, 10).
FORMULA
a(n) = 3*a(n-1) + 10*a(n-2).
a(n) = (5^n - (-2)^n)/7. Binomial transform is A015540. - Paul Barry, Feb 07 2004
G.f.: x/(1-x*(10*x+3)). - Harvey P. Dale, Jan 27 2012
MATHEMATICA
Join[{a=0, b=1}, Table[c=3*b+10*a; a=b; b=c, {n, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 16 2011 *)
LinearRecurrence[{3, 10}, {0, 1}, 30] (* or *) CoefficientList[Series[x/(1-x (10x+3)), {x, 0, 29}], x] (* Harvey P. Dale, Jan 27 2012 *)
PROG
(Sage) [lucas_number1(n, 3, -10) for n in range(0, 23)]# Zerinvary Lajos, Apr 22 2009
(Magma) [5^n/7-(-2)^n/7: n in [0..30]]; // Vincenzo Librandi, Aug 23 2011
(PARI) for(n=0, 30, print1((5^n - (-2)^n)/7, ", ")) \\ G. C. Greubel, Jan 01 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved