A103193 - OEIS

%I #21 Jan 12 2025 21:01:29

%S 0,1,1,1,1,1,5,1,-5,-7,1,-1,33,1,-1,-255,1,255,1,1,-2049,16385,1,

%T -32769,262145,1,-524289,1,1,-8388609,-268435455,1,268435455,

%U 8589934593,1,-1,-549755813887,1,-1,70368744177665,1,-70368744177665,1,1,9007199254740991,-1152921504606846975

%N A sequence of triples arising from a matrix calculation, in particular let m = floor(n/3), then (a(3*m), a(3*m+1), a(3*m+2)) = M^(m*(m+1)/n) * (0, 1, 1) where M is the matrix [[2,0,1], [0,1,0], [-2,1,0]].

%t a = 1;

%t M1 = {{2, 0, 1}, {a - 1, a, 0}, {a - 3, 1, a - 1}};

%t v[0] = {0, 1, 1}; v[1] = {1, 1, 1};

%t v[n_] := v[n] = MatrixPower[M1, n].v[n - 1];

%t b = Flatten[Table[v[n], {n, 0, 15}]]

%Y Cf. A103191.

%K sign,less

%O 0,7

%A _Roger L. Bagula_, Mar 18 2005