A295675 - OEIS

%I #6 Nov 28 2017 10:30:21

%S 1,1,2,-2,0,3,3,1,4,10,14,19,33,57,90,142,232,379,611,985,1596,2586,

%T 4182,6763,10945,17713,28658,46366,75024,121395,196419,317809,514228,

%U 832042,1346270,2178307,3524577,5702889,9227466,14930350,24157816,39088171

%N a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 1, a(2) = 2, a(3) = -2.

%C Lim_{n->inf} a(n)/a(n-1) = (1 + sqrt(5))/2 = golden ratio (A001622), so that a( ) has the growth rate of the Fibonacci numbers (A000045).

%H Clark Kimberling, <a href="/A295675/b295675.txt">Table of n, a(n) for n = 0..2000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 1, 1)

%F a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 1, a(2) = 2, a(3) = -2.

%F G.f.: (-1 - x^2 + 5 x^3)/(-1 + x + x^3 + x^4).

%t LinearRecurrence[{1, 0, 1, 1}, {1, 1, 2, -2}, 100]

%Y Cf. A001622, A000045.

%K easy,sign

%O 0,3

%A _Clark Kimberling_, Nov 27 2017