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A295672 a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 1, a(2) = 1, a(3) = -2. 1

%I

%S 1,1,1,-2,0,2,1,-1,1,4,4,4,9,17,25,38,64,106,169,271,441,716,1156,

%T 1868,3025,4897,7921,12814,20736,33554,54289,87839,142129,229972,

%U 372100,602068,974169,1576241,2550409,4126646,6677056,10803706,17480761,28284463

%N a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 1, a(2) = 1, 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="/A295672/b295672.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) = 1, a(3) = -2.

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

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

%Y Cf. A001622, A000045.

%K easy,sign

%O 0,4

%A _Clark Kimberling_, Nov 27 2017

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Last modified May 27 02:13 EDT 2022. Contains 354092 sequences. (Running on oeis4.)