All linear fourth-order sequences are a linear combination of these four sequences.
1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 4, 4, 4, 6, 7, 8, 8, 12, 14, 15, 15, 23, 27, 29, 29, 44, 52, 56, 56, 85, 100, 108, 108, 164, 193, 208, 208, 316, 372, 401, 401, 609, 717, 773, 773, 1174, 1382, 1490, 1490, 2263, 2664, 2872, 2872, 4362, 5135, 5536, 5536, 8408, 9898
1
Note that the 4-th row is the first row shifted by one.
T. D. Noe, Plot of 75 quadruples
T. D. Noe, Table of 75 quadruples
Eric W. Weisstein, MathWorld: Linear Recurrence Equation
(Mma) nn = 4; 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. A000078, A001630, A001631, S000822-S000831.
nonn,tabl
T. D. Noe, Jan 15 2016