OFFSET
0,2
COMMENTS
a(n)/a(n-1) tends to phi, 1.6180339...; e.g. a(16)/a(15) = 2592/1604 = 1.6159...
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2, 1, -3, 0, 1)
FORMULA
G.f.: ( -1+x^3+x^2 ) / ( (1+x)*(x^2+x-1)*(x-1)^2 ). - R. J. Mathar, Mar 03 2013
a(n) = 2*a(n-1) + a(n-2) - 3*a(n-3) + a(n-5). - Andrew Howroyd, Aug 10 2018
EXAMPLE
a(4) = 10 = (1 + 4 + 1 + 3 + 1).
PROG
(PARI) a(n) = fibonacci(n+2) + n\2; \\ Andrew Howroyd, Aug 10 2018
(PARI) Vec((1 - x^2 - x^3)/((1 - x)^2*(1 + x)*(1 - x - x^2)) + O(x^40)) \\ Andrew Howroyd, Aug 10 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Gary W. Adamson & Mats Granvik, Oct 31 2009
EXTENSIONS
Name changed and terms a(17) and beyond from Andrew Howroyd, Aug 10 2018
STATUS
approved