A152269 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.

0, 1, -3, -13, 15, 97, -171, -901, 1335, 7609, -12147, -66877, 103455, 577873, -905979, -5029429, 7840455, 43639081, -68193603, -379137133, 591862575, 3292136257, -5141508171, -28593069541, 44647143255, 248313707929

Offset

0,3

Comments

Characteristic Polynomial is: 8 - 7 x + x^2.

Binary switching of the IdentityMatrix[2] uncovers opposite signed based on

A006131 with characteristic polynomial -4 - x + x^2

Links

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (0,-5,0,32).

Formula

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):

a(n) first element of -v(n)[[1]]/2.

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]

Mathematica

Clear[M, M0, Mh, v];
M0 = {{0, 1}, {1, 1/2}}; M = {{0, 2}, {2, 1}};
Mh[n_] := M0.(M.Inverse[Mod[n, 2]*IdentityMatrix[2] + M0]);
v[0] = {0, 1};
v[n_] := v[n] = Mh[n].v[n - 1]
Table[ -v[n][[1]]/2, {n, 0, 30}]

Crossrefs

A006131

Sequence in context: A340018 A216044 A023144 * A063674 A273678 A022124

Adjacent sequences: A152266 A152267 A152268 * A152270 A152271 A152272

Keyword

sign,easy

Author

Roger L. Bagula, Dec 01 2008

Status

approved