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4 X infinity array read by rows: let M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 1, 0}}, w[0] = {0, 0, 1, 1}', w[n]' = M*w[n -1]'; the n-th row of the array is w[n]' (the prime denotes transpose).
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%I #11 Sep 05 2023 18:26:01

%S 0,0,1,1,0,1,1,1,1,1,1,1,1,1,1,2,1,1,2,2,1,2,2,3,2,2,3,3,2,3,3,5,3,3,

%T 5,5,3,5,5,8,5,5,8,8,5,8,8,13,8,8,13,13,8,13,13,21,13,13,21,21,13,21,

%U 21,34,21,21,34,34,21,34,34,55,34,34,55,55,34,55,55,89,55,55,89,89,55,89

%N 4 X infinity array read by rows: let M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 1, 0}}, w[0] = {0, 0, 1, 1}', w[n]' = M*w[n -1]'; the n-th row of the array is w[n]' (the prime denotes transpose).

%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1).

%F From _Chai Wah Wu_, Sep 05 2023: (Start)

%F a(n) = a(n-8) + a(n-16) for n > 15.

%F G.f.: x^2*(-x^13 - x^10 - x^7 - x^6 - x^5 - x^4 - x^3 - x - 1)/(x^16 + x^8 - 1). (End)

%t M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 1, 0}} w[0] = {0, 0, 1, 1} w[n_] := w[n] = M.w[n - 1] a = Flatten[Table[w[n], {n, 0, Floor[200/4]}]] (* polynomial*) Det[M - x*IdentityMatrix[4]] Solve[Det[M - x*IdentityMatrix[4]] == 0, x]

%K nonn,tabf

%O 0,16

%A _Roger L. Bagula_, Mar 24 2005

%E Edited by _N. J. A. Sloane_, Sep 24 2006