login
A295861
a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -2, a(1) = -1, a(2) = 0, a(3) = 1.
1
-2, -1, 0, 1, 7, 12, 31, 51, 106, 173, 327, 532, 955, 1551, 2698, 4377, 7459, 12092, 20319, 32923, 54778, 88725, 146575, 237348, 390067, 631511, 1033866, 1673569, 2732011, 4421964, 7203127, 11657859, 18959290, 30682685, 49838583, 80652340, 130884139
OFFSET
0,1
COMMENTS
a(n)/a(n-1) -> (1 + sqrt(5))/2 = golden ratio (A001622), so that a( ) has the growth rate of the Fibonacci numbers (A000045).
FORMULA
a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = -2, a(1) = -1, a(2) = 0, a(3) = 1.
G.f.: (-2 + x + 7 x^2)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).
MATHEMATICA
LinearRecurrence[{1, 3, -2, -2}, {-2, -1, 0, 1}, 100]
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Clark Kimberling, Jan 07 2018
STATUS
approved