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%I A069005 #17 Jun 04 2019 11:39:49
%S A069005 1,7,19,56,160,462,1329,3828,11021,31735,91376,263108,757588,2181389,
%T A069005 6281058,18085587,52075371,149945056,431749580,1243173370,3579575053,
%U A069005 10306975580,29677753369,85453685055,246054079584,708484485384
%N A069005 Let M = 4 X 4 matrix with rows /1,1,1,1/1,1,1,0/1,1,0,0/1,0,0,0/ and A(n) = vector (x(n),y(n),z(n),t(n)) = M^n*A where A is the vector (1,1,1,1); then a(n)=z(n).
%C A069005 a(n) = A091024(n+1) for n > 1. - _Georg Fischer_, Oct 19 2018
%H A069005 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,-1,-1).
%F A069005 G.f.: x*(-x^4-2*x^3+2*x^2+5*x+1)/((1+x)*(1-3*x+x^3)). [Corrected by _Georg Fischer_, May 24 2019]
%t A069005 CoefficientList[Series[x (-x^4 - 2 x^3 + 2 x^2 + 5 x + 1)/((1 + x) (1 - 3 x + x^3)), {x, 0, 40}], x] (* _Georg Fischer_, May 24 2019 *)
%Y A069005 Cf. A018919, A091024.
%K A069005 nonn,easy
%O A069005 1,2
%A A069005 _Benoit Cloitre_, Apr 02 2002

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