tribo[n_, a_, b_, c_] := tribo[n - 1, b, c, a + b + c]
tribo[0, a_, b_, c_] := a
tribo[n_] := tribo[n, 0, 1, 1]

seq1 = Table[tribo[x], {x, 0, 14}]
{0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705}

quadra4[n_, a_, b_, c_, d_] := quadra4[n - 1, b, c, d, a + b + c + d]
quadra4[0, a_, b_, c_, d_] := a
quadra4[n_] := quadra4[n, 0, 1, 1, 1]

seq2 = Table[quadra4[x], {x, 0, 14}]
{0, 1, 1, 1, 3, 6, 11, 21, 41, 79, 152, 293, 565, 1089, 2099}