# Fibonacci n-step number sequences

### Lazy List with Closure

```perl
sub nacci ( $s = 2, :@start = (1,) ) {
    my @seq = |@start, { state $n = +@start; @seq[ ($n - $s .. $n++ - 1).grep: * >= 0 ].sum } … *;
}

put "{.fmt: '%2d'}-nacci: ", nacci($_)[^20] for 2..12 ;

put "Lucas: ", nacci(:start(2,1))[^20];
```

#### Output:

```
 2-nacci: 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
 3-nacci: 1 1 2 4 7 13 24 44 81 149 274 504 927 1705 3136 5768 10609 19513 35890 66012
 4-nacci: 1 1 2 4 8 15 29 56 108 208 401 773 1490 2872 5536 10671 20569 39648 76424 147312
 5-nacci: 1 1 2 4 8 16 31 61 120 236 464 912 1793 3525 6930 13624 26784 52656 103519 203513
 6-nacci: 1 1 2 4 8 16 32 63 125 248 492 976 1936 3840 7617 15109 29970 59448 117920 233904
 7-nacci: 1 1 2 4 8 16 32 64 127 253 504 1004 2000 3984 7936 15808 31489 62725 124946 248888
 8-nacci: 1 1 2 4 8 16 32 64 128 255 509 1016 2028 4048 8080 16128 32192 64256 128257 256005
 9-nacci: 1 1 2 4 8 16 32 64 128 256 511 1021 2040 4076 8144 16272 32512 64960 129792 259328
10-nacci: 1 1 2 4 8 16 32 64 128 256 512 1023 2045 4088 8172 16336 32656 65280 130496 260864
11-nacci: 1 1 2 4 8 16 32 64 128 256 512 1024 2047 4093 8184 16364 32720 65424 130816 261568
12-nacci: 1 1 2 4 8 16 32 64 128 256 512 1024 2048 4095 8189 16376 32748 65488 130960 261888
Lucas: 2 1 3 4 7 11 18 29 47 76 123 199 322 521 843 1364 2207 3571 5778 9349
```

### Generative

A slightly more straight forward way of constructing a lazy list.

```perl
sub fib ($n, @xs is copy = [1]) {
    flat gather {
        take @xs[*];
        loop {
            take my $x = [+] @xs;
            @xs.push: $x;
            @xs.shift if @xs > $n;
        }
    }
}

for 2..10 -> $n {
    say fib($n, [1])[^20];
}
say fib(2, [2,1])[^20];
```
