A295671 - OEIS

%I #12 Apr 02 2020 14:06:36

%S 1,1,1,-1,1,3,3,3,7,13,19,29,49,81,129,207,337,547,883,1427,2311,3741,

%T 6051,9789,15841,25633,41473,67103,108577,175683,284259,459939,744199,

%U 1204141,1948339,3152477,5100817,8253297,13354113,21607407,34961521,56568931

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

%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="/A295671/b295671.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) = -1.

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

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

%Y Cf. A001622, A000045.

%K easy,sign

%O 0,6

%A _Clark Kimberling_, Nov 27 2017