A103191 - OEIS

%I #24 Jan 12 2025 21:01:19

%S 0,1,1,1,1,1,2,4,0,8,12,4,40,72,24,352,640,192,4736,8704,2560,98816,

%T 181760,53760,3186688,5861376,1732608,158629888,291766272,86245376,

%U 12189433856,22419865600,6627262464,1445910806528,2659444588544

%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 [[1,0,1], [1,1,0], [-1,1,0]].

%t a = 1;

%t M1 = {{1, 0, 1}, {a, a, 0}, {a - 2, 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, 11}]]

%Y Cf. A103193.

%K nonn,less

%O 0,7

%A _Roger L. Bagula_, Mar 18 2005