Fibonacci n-step number sequences

This page is the answer to the task Fibonacci n-step number sequences in the Rosetta Code.

For $\text{[math]}$ we have the Fibonacci sequence; with initial values $\text{[math]}$ and $\text{[math]}$
For $\text{[math]}$ we have the tribonacci sequence; with initial values $\text{[math]}$ and $\text{[math]}$
For $\text{[math]}$ we have the tetranacci sequence; with initial values $\text{[math]}$ and $\text{[math]}$
...
For general $\text{[math]}$ we have the Fibonacci $\text{[math]}$ -step sequence - $\text{[math]}$ ; with initial values of the first $\text{[math]}$ values of the $\text{[math]}$ 'th Fibonacci $\text{[math]}$ -step sequence $\text{[math]}$ ; and $\text{[math]}$ 'th value of this $\text{[math]}$ 'th sequence being $\text{[math]}$

For small values of $\text{[math]}$ , Greek numeric prefixes are sometimes used to individually name each series.

Fibonacci $\text{[math]}$ -step sequences
$\text{[math]}$	Series name	Values
2	fibonacci	1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 ...
3	tribonacci	1 1 2 4 7 13 24 44 81 149 274 504 927 1705 3136 ...
4	tetranacci	1 1 2 4 8 15 29 56 108 208 401 773 1490 2872 5536 ...
5	pentanacci	1 1 2 4 8 16 31 61 120 236 464 912 1793 3525 6930 ...
6	hexanacci	1 1 2 4 8 16 32 63 125 248 492 976 1936 3840 7617 ...
7	heptanacci	1 1 2 4 8 16 32 64 127 253 504 1004 2000 3984 7936 ...
8	octonacci	1 1 2 4 8 16 32 64 128 255 509 1016 2028 4048 8080 ...
9	nonanacci	1 1 2 4 8 16 32 64 128 256 511 1021 2040 4076 8144 ...
10	decanacci	1 1 2 4 8 16 32 64 128 256 512 1023 2045 4088 8172 ...

Allied sequences can be generated where the initial values are changed: The Lucas series sums the two preceding values like the fibonacci series for $\text{[math]}$ but uses $\text{[math]}$ as its initial values.

Task

Write a function to generate Fibonacci $\text{[math]}$ -step number sequences given its initial values and assuming the number of initial values determines how many previous values are summed to make the next number of the series.
Use this to print and show here at least the first ten members of the Fibo/tribo/tetra-nacci and Lucas sequences.

Solution

Main function

According to the requirements, the program must generate a series, and the order (Fibonacci, Tribonacci, etc) should be determined according with the initial values.

In this case, the number n indicates how many terms of the series will be generated.

The following generates a Fibonacci series of 20 terms:

The following generates a Lucas series of 20 terms:

The following generates a Tribonacci series of 20 terms:

Generating initial values

The initial values can be generated by the following function.

Note that it is a recursive function, and it calls the previously defined function. It requires the initial values as a seed, $\text{[math]}$ for Fibonacci style (Fibonacci, Tribonacci, etc), and $\text{[math]}$ for Lucas style.