All linear fifth-order sequences are a linear combination of these five sequences.
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 6, 7, 8, 8, 8, 12, 14, 15, 16, 16, 24, 28, 30, 31, 31, 47, 55, 59, 61, 61, 92, 108, 116, 120, 120, 181, 212, 228, 236, 236, 356, 417, 448, 464, 464, 700, 820, 881, 912, 912, 1376, 1612, 1732, 1793, 1793, 2705
1
Note that the 5-th row is the first row shifted by one.
T. D. Noe, Plot of 60 quintuples
T. D. Noe, Table of 60 quintuples
Eric W. Weisstein, MathWorld: Linear Recurrence Equation
(Mma) nn = 5; 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. A001591, A124312, A124313, A251653, S000822-S000831.
nonn,tabl
T. D. Noe, Jan 15 2016