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 A295855 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = -2, a(2) = 2, a(3) = 1. 1

%I #7 Aug 27 2021 21:15:39

%S 1,-2,2,1,9,12,33,49,106,163,317,496,909,1437,2538,4039,6961,11128,

%T 18857,30241,50634,81387,135093,217504,358741,578293,949322,1531711,

%U 2505609,4045512,6600273,10662169,17360746,28055683,45613037,73734256,119740509,193605837

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

%C 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="/A295855/b295855.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, 3, -2, -2)

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

%F G.f.: (1 - 3 x + x^2 + 7 x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).

%t LinearRecurrence[{1, 3, -2, -2}, {1, -2, 2, 1}, 100]

%Y Cf. A001622, A000045.

%K easy,sign

%O 0,2

%A _Clark Kimberling_, Dec 01 2017

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Last modified August 12 13:41 EDT 2024. Contains 375113 sequences. (Running on oeis4.)