All linear third-order sequences are a linear combination of these three sequences.
1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 6, 7, 7, 11, 13, 13, 20, 24, 24, 37, 44, 44, 68, 81, 81, 125, 149, 149, 230, 274, 274, 423, 504, 504, 778, 927, 927, 1431, 1705, 1705, 2632, 3136, 3136, 4841, 5768, 5768, 8904, 10609, 10609, 16377, 19513, 19513, 30122, 35890
1
Note that the 3-th row is the first row shifted by one.
T. D. Noe, Plot of 100 triples
T. D. Noe, Table of 100 triples
Eric W. Weisstein, MathWorld: Linear Recurrence Equation
(Mma) nn = 3; t = IdentityMatrix[nn]; Do[AppendTo[t, Sum[t[[k - i]], {i, nn}]], {k, nn + 1, nn + 60/nn}]; t = Drop[Flatten[t], nn^2]; t
Cf. A000073, A001590, S000822-S000831.
nonn,tabl
T. D. Noe, Jan 15 2016