cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A295722 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -1, a(1) = -1, a(2) = 2, a(3) = 3.

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%I A295722 #6 Aug 27 2021 21:20:40
%S A295722 -1,-1,2,3,13,20,49,77,158,251,473,756,1357,2177,3790,6095,10397,
%T A295722 16748,28169,45429,75646,122099,201841,325988,536021,866105,1418510,
%U A295722 2292807,3744085,6053276,9862897,15948941,25942910,41957387,68162441,110250900,178937629
%N A295722 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -1, a(1) = -1, a(2) = 2, a(3) = 3.
%C A295722 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 A295722 Clark Kimberling, <a href="/A295722/b295722.txt">Table of n, a(n) for n = 0..2000</a>
%H A295722 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1, 3, -2, -2)
%F A295722 a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = -1, a(1) = -2, a(2) = 2, a(3) = 3.
%F A295722 G.f.: (-1 + 6 x^2 + 2 x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).
%t A295722 LinearRecurrence[{1, 3, -2, -2}, {-1, -1, 2, 3}, 100]
%Y A295722 Cf. A001622, A000045, A005672.
%K A295722 easy,sign
%O A295722 0,3
%A A295722 _Clark Kimberling_, Nov 29 2017