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FORMULA
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M2={{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 4}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 4}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 4}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 4, 2, 4, 4, 8}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2}, {0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 2, 4}, {0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 4}, {0, 0, 0, 0, 1, 2, 2, 4, 0, 0, 0, 0, 2, 4, 4, 8}, {0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 4}, {0, 0, 1, 2, 0, 0, 2, 4, 0, 0, 2, 4, 0, 0, 4, 8}, {0, 1, 0, 2, 0, 2, 0, 4, 0, 2, 0, 4, 0, 4, 0, 8}, {1, 2, 2, 4, 2, 4, 4, 8, 2, 4, 4, 8, 4, 8, 8, 16}} v[1] = Table[1, {n, 0, 15}] v[n_] := v[n] = M2.v[n - 1] a(n) = v[n][[1]]
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MATHEMATICA
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a = {{0, 1}, {1, 2}}; t[n_, m_] := a[[n, m]]; a = Table[t[n, m]*t[i, j], {n, 1, 2}, {m, 1, 2}, {i, 1, 2}, {j, 1, 2}]; M = Flatten[Table[{Flatten[Table[a[[ n, m]][[1, i]], {n, 1, 2}, {i, 1, 2}]], Flatten[Table[a[[n, m]][[2, i]], {n, 1, 2}, {i, 1, 2}]]}, {m, 1, 2}], 1]; aa = Table[M[[n, m]]*M[[i, j]], {n, 1, 4}, {m, 1, 4}, {i, 1, 4}, {j, 1, 4}]; M2 = Flatten[Table[{Flatten[Table[aa[[ n, m]][[1, i]], {n, 1, 4}, {i, 1, 4}]], Flatten[Table[aa[[n, m]][[2, i]], {n, 1, 4}, {i, 1, 4}]], Flatten[Table[aa[[ n, m]][[3, i]], {n, 1, 4}, {i, 1, 4}]], Flatten[Table[aa[[ n, m]][[4, i]], {n, 1, 4}, {i, 1, 4}]]}, {m, 1, 4}], 1]; v[1] = Table[1, {n, 0, 15}]; v[n_] := v[n] = M2.v[n - 1]; a = Table[v[n][[1]], {n, 1, 50}]
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