my @even   = 0, 2, 4 ... { $_ + 2};
my @powers = 1, 2, 4 ... { $_ * 2 };
my @fib    = 1, 1, 2 ... { $^a + $^b};

##</code><code>##

my @ints   = 1, 2, 3, 4 ... *;
my @even   = 0, 2, 4, 6 ... *;
my @powers = 1, 2, 4, 8 ... *;

##</code><code>##

1, 3, 5 ... *		# odd numbers
1, 2, 4 ... *		# powers of 2
    
##</code><code>##

sub series(@items, $recursion_level = 2) {
    return if $recursion_level < 0;
    return if @items < 2;
    
    # are all items the same?
    return @items[0] if [==] @items;

    # detect arithmetic sequences
    my @diffs = map { @items[$_+1] - @items[$_] }, 0 .. (@items - 2);
    my $d = series(@diffs, $recursion_level - 1);
    return @items[*-1] + $d if $d.defined;

    # detect geometric sequences
    my $r = try {
        my @ratios = map { @items[$_+1] / @items[$_] }, 0 .. (@items - 2);
        series(@ratios, $recursion_level - 1);
    }
    return @items[*-1] * $r if $r.defined;

    # give up
    return;
}

##</code><code>##

use List::MoreUtils qw(all);
sub series {
    _series(2, @_);
}

sub _series {
    my $recursion_level = shift;
    return if $recursion_level < 0;
    return if @_ < 2;
    my $first = $_[0];
    if (all { $_ == $first } @_) {
        return $first;
    }

    my @a = map { $_[$_+1] - $_[$_] } 0 .. (@_ - 2);
    my $r = _series($recursion_level - 1, @a);
    return $_[-1] + $r if defined $r;

    # catch division by zero
    $r = eval {
        @a = map { $_[$_+1] / $_[$_] } 0 ... (@_ - 2);
        _series($recursion_level - 1, @a);
    };
    return $_[-1] * $r if defined $r;

    return;
}


##</code><code>##

#!/usr/bin/perl
use strict;
use warnings;

use Test::More qw(no_plan);

sub series {
    # your code here.
}

my @tests = (
    [[1],                   undef],
    [[1, 1],                1],
    [[0, 0],                0],
    [[1, 2],                undef],
    [[0, 1, 2],             3],
    [[1, 0, -1],            -2],
    [[1, 2, 3],             4],
    [[1, 2, 4],             8],     # powers
    [[2, 4, 8],             16],
    [[1, 3, 9],             27],
    [[1, -1, 1, -1],        1],     # alternations
    [[-1, 1, -1, 1],        -1],
    [[1, 0, 1, 0],          1],
    [[0, 1, 0, 1],          0],
    [[1, 1, 2, 3, 5],       8],     # fibonacci
    [[0, 1, 1, 2, 3],       8],
    [[1, 2, 3, 5, 8],       13],
    [[1, 2, 6, 24, 120],    720],   # factorials
    [[1, 0, 0, 1],          undef],
    [[1, 2, 3, 1],          undef],
);

for my $t (@tests) {
    my $expected = defined $t->[1] ? $t->[1] : 'undef';
    my $result   = series(@{$t->[0]});
    $result = 'undef' unless defined $result;
    is $result, $expected, "seq " . join(', ', @{$t->[0]});
}