Let M0 = {{2, 2, 0}, {1, 0, 1}, {0, 2, 2}}; M1 = {{1, 0, 1}, {2, 2, 0}, {0, 2, 2}}; M2 = {{2, 2, 0}, {0, 2, 2}, {1, 0, 1}}; M[n_] := M[n] = If[Mod[v[n][[1]], 3] == 0, M1, If[Mod[v[n][[2]], 3] == 0, M0, M2]] v[0] = {1, 1, 1}; M[0] = {{2, 2, 0}, {1, 0, 1}, {0, 2, 2}}; v[n_] := v[n] = M[n - 1].v[n - 1]. Then a(n) =v[n][[1]].
A115106
Let M0 = {{2, 2, 0}, {1, 0, 1}, {0, 2, 2}}; M1 = {{1, 0, 1}, {2, 2, 0}, {0, 2, 2}}; M2 = {{2, 2, 0}, {0, 2, 2}, {1, 0, 1}}; M[n_] := M[n] = If[Mod[v[n][[1]], 3] == 0, M1, If[Mod[v[n][[2]], 3] == 0, M0, M2]] v[0] = {1, 1, 1}; M[0] = {{2, 2, 0}, {1, 0, 1}, {0, 2, 2}}; v[n_] := v[n] = M[n - 1].v[n - 1]. Then a(n) =v[n][[1]].
Terms
- a(0) =1a(1) =4a(2) =12a(3) =20a(4) =136a(5) =392a(6) =1408a(7) =4544a(8) =15040a(9) =48896a(10) =159232a(11) =516608a(12) =1675264a(13) =5427200a(14) =17575936a(15) =56901632a(16) =184188928a(17) =596148224a(18) =1929379840a(19) =6244007936a(20) =20206845952a(21) =65392345088a(22) =211617316864a(23) =684814499840
External references
- oeis: A115106