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%I #11 Jun 13 2015 00:52:44
%S 0,1,-3,-13,15,97,-171,-901,1335,7609,-12147,-66877,103455,577873,
%T -905979,-5029429,7840455,43639081,-68193603,-379137133,591862575,
%U 3292136257,-5141508171,-28593069541,44647143255,248313707929
%N A switched hidden Markov recursion involving the matrices: M0 = {{0, 1}, {1, 1/2}}; M = {{0, 2}, {2, 1}}; as Mh=M0.M.(M0+I*mod[n.2]); v[(n)=Mh.v(n-1): first element of v.
%C Characteristic Polynomial is: 8 - 7 x + x^2.
%C Binary switching of the IdentityMatrix[2] uncovers opposite signed based on
%C A006131 with characteristic polynomial -4 - x + x^2
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,-5,0,32).
%F M0 = {{0, 1}, {1, 1/2}}; M = {{0, 2}, {2, 1}};
%F as Mh=M0.M.(M0+I*mod[n.2]); v[(n)=Mh.v(n-1):
%F a(n) first element of -v(n)[[1]]/2.
%F a(n)=5*a(n-2)+32*a(n-4). G.f.: x(1+3x+8x^2)/(1-5x^2-32x^4). [From _R. J. Mathar_, Dec 04 2008]
%t Clear[M, M0, Mh, v];
%t M0 = {{0, 1}, {1, 1/2}}; M = {{0, 2}, {2, 1}};
%t Mh[n_] := M0.(M.Inverse[Mod[n, 2]*IdentityMatrix[2] + M0]);
%t v[0] = {0, 1};
%t v[n_] := v[n] = Mh[n].v[n - 1]
%t Table[ -v[n][[1]]/2, {n, 0, 30}]
%Y A006131
%K sign,easy
%O 0,3
%A _Roger L. Bagula_, Dec 01 2008
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