A103193 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]].

0, 1, 1, 1, 1, 1, 5, 1, -5, -7, 1, -1, 33, 1, -1, -255, 1, 255, 1, 1, -2049, 16385, 1, -32769, 262145, 1, -524289, 1, 1, -8388609, -268435455, 1, 268435455, 8589934593, 1, -1, -549755813887, 1, -1, 70368744177665, 1, -70368744177665, 1, 1, 9007199254740991, -1152921504606846975

Offset

0,7

Links

Table of n, a(n) for n=0..45.

Mathematica

a = 1;
M1 = {{2, 0, 1}, {a - 1, a, 0}, {a - 3, 1, a - 1}};
v[0] = {0, 1, 1}; v[1] = {1, 1, 1};
v[n_] := v[n] = MatrixPower[M1, n].v[n - 1];
b = Flatten[Table[v[n], {n, 0, 15}]]

Crossrefs

Cf. A103191.

Sequence in context: A054244 A093562 A081774 * A011093 A062176 A338167

Adjacent sequences: A103190 A103191 A103192 * A103194 A103195 A103196

Keyword

sign,less

Author

Roger L. Bagula, Mar 18 2005

Status

approved