1,5

Needs to be extended to the 27 X 27 level, but that is a long process by hand right now. This is the next Hadamard level up from the 2 X 2 -> 2^n to the 3 X 3 -> 3^n level matrices.

MA = {{0, 1, 0}, {0, 0, 1}, {1, 1, 0}}; MB = {{0, 0, 1}, {0, 1, 0},{1, 0, -1}}; With substitution rule: m[n]->If[m[n - 1][[i, j]] == 0, {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}}, If[m[n - 1][[i, j]] == 1, MA, MB]];

{1},

{1, -1},

{-1, 2, 0, -1},

{-1, -1, 3, 4, -4, -7, 1, 5, 0, -1}

MA = {{0, 1, 0}, {0, 0, 1}, {1, 1, 0}}; MB = {{0, 0, 1}, {0, 1, 0}, {1, 0, -1}}; m[0] = {{1}} m[1] = {{0, 0, 1}, {0, 1, 0}, {1, 0, -1}}; m[2] = {{0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 0, 1, 1, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 1, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0, 1}, {0, 0, 1, 0, 0, 0, 0, 1, 0}, {1, 1, 0, 0, 0, 0, 1, 0, -1}}; m[n_] := Table[Table[If[m[n - 1][[i, j]] == 0, {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}}, If[m[n - 1][[i, j]] == 1, MA, MB]], {j, 1, 3^(n - 1)}], {i, 1, 3^(n - 1)}]; TableForm[m[3]] Table[CharacteristicPolynomial[m[i], x], {i, 0, 2}] a = Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[m[i], x], x], {i, 0, 2}]]; Flatten[a] (* visualization*) Table[ListDensityPlot[m[i]], {i, 0, 3}]

Adjacent sequences: A134652 A134653 A134654 this_sequence A134656 A134657 A134658

Sequence in context: A029394 A035467 A024996 this_sequence A077614 A116948 A101660

uned,probation,sign

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 25 2008