login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A295853 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) = 2, a(3) = 1. 1

%I

%S -2,-1,2,1,13,14,47,61,148,209,437,646,1243,1889,3452,5341,9433,14774,

%T 25487,40261,68308,108569,181997,290566,482803,773369,1276652,2050021,

%U 3367633,5417654,8867207,14284861,23315908,37600769,61244357,98845126,160744843

%N 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) = 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="/A295853/b295853.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) = -2, a(1) = -1, a(2) = 2, a(3) = 1.

%F G.f.: (-2 + x + 9 x^2 - 2 x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).

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

%Y Cf. A001622, A000045.

%K easy,sign

%O 0,1

%A _Clark Kimberling_, Dec 01 2017

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 1 10:37 EDT 2021. Contains 346385 sequences. (Running on oeis4.)