OFFSET
0,2
COMMENTS
a(n)/a(n-1) tends to 3.30277563... = exp(ArcSinh(3/2)) (A098316).
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-6,1,1).
FORMULA
O.g.f.: (1 - x + x^2)/((1-x)^2*(1 - 3*x - x^2)). - R. J. Mathar, Mar 17 2008
MATHEMATICA
LinearRecurrence[{5, -6, 1, 1}, {1, 4, 15, 52}, 30] (* Harvey P. Dale, Mar 21 2018 *)
PROG
(Magma) I:=[1, 4, 15, 52]; [n le 4 select I[n] else 5*Self(n-1) -6*Self(n-2) +Self(n-3) +Self(n-4): n in [1..31]]; // G. C. Greubel, Oct 22 2021
(Sage) [(2*lucas_number1(n+2, 3, -1) + 8*lucas_number1(n+1, 3, -1) - 3*n -5)/9 for n in (0..30)] # G. C. Greubel, Oct 22 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Apr 02 2006
EXTENSIONS
More terms from R. J. Mathar, Mar 17 2008
STATUS
approved