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A295678 a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 2, a(2) = 1, a(3) = 3.

%I A295678 #9 Apr 26 2022 07:11:48
%S A295678 1,2,1,3,6,9,13,22,37,59,94,153,249,402,649,1051,1702,2753,4453,7206,
%T A295678 11661,18867,30526,49393,79921,129314,209233,338547,547782,886329,
%U A295678 1434109,2320438,3754549,6074987,9829534,15904521,25734057,41638578,67372633,109011211
%N A295678 a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 2, a(2) = 1, a(3) = 3.
%C A295678 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 A295678 Clark Kimberling, <a href="/A295678/b295678.txt">Table of n, a(n) for n = 0..2000</a>
%H A295678 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 1, 1)
%F A295678 a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 2, a(2) = 1, a(3) = 3.
%F A295678 G.f.: (-1 - x + x^2 - x^3)/( (x^2+x-1)*(1+x^2)).
%F A295678 5*a(n) = A022098(n)+2*( A000034(n+1)*(-1)^floor(n/2)). - _R. J. Mathar_, Apr 26 2022
%t A295678 LinearRecurrence[{1, 0, 1, 1}, {1, 2, 1, 3}, 100]
%Y A295678 Cf. A001622, A000045.
%K A295678 nonn,easy
%O A295678 0,2
%A A295678 _Clark Kimberling_, Nov 27 2017