Task: Fibonacci n-step number sequences
C#: using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace Fibonacci
{
    class Program
    {
        static void Main(string[] args)
        {
            PrintNumberSequence("Fibonacci", GetNnacciNumbers(2, 10));
            PrintNumberSequence("Lucas", GetLucasNumbers(10));
            PrintNumberSequence("Tribonacci", GetNnacciNumbers(3, 10));
            PrintNumberSequence("Tetranacci", GetNnacciNumbers(4, 10));
            Console.ReadKey();
        }

        private static IList<ulong> GetLucasNumbers(int length)
        {
            IList<ulong> seedSequence = new List<ulong>() { 2, 1 };
            return GetFibLikeSequence(seedSequence, length);
        }

        private static IList<ulong> GetNnacciNumbers(int seedLength, int length)
        {
            return GetFibLikeSequence(GetNacciSeed(seedLength), length);
        }

        private static IList<ulong> GetNacciSeed(int seedLength)
        {
            IList<ulong> seedSquence = new List<ulong>() { 1 };

            for (uint i = 0; i < seedLength - 1; i++)
            {
                seedSquence.Add((ulong)Math.Pow(2, i));
            }

            return seedSquence;
        }

        private static IList<ulong> GetFibLikeSequence(IList<ulong> seedSequence, int length)
        {
            IList<ulong> sequence = new List<ulong>();

            int count = seedSequence.Count();

            if (length <= count)
            {
                sequence = seedSequence.Take((int)length).ToList();
            }
            else
            {
                sequence = seedSequence;

                for (int i = count; i < length; i++)
                {
                    ulong num = 0;

                    for (int j = 0; j < count; j++)
                    {
                        num += sequence[sequence.Count - 1 - j];
                    }

                    sequence.Add(num);
                }
            }

            return sequence;
        }

        private static void PrintNumberSequence(string Title, IList<ulong> numbersequence)
        {
            StringBuilder output = new StringBuilder(Title).Append("   ");

            foreach (long item in numbersequence)
            {
                output.AppendFormat("{0}, ", item);
            }

            Console.WriteLine(output.ToString());
        }
    }
}

Python: >>> def fiblike(start):
	addnum = len(start)
	memo = start[:]
	def fibber(n):
		try:
			return memo[n]
		except IndexError:
			ans = sum(fibber(i) for i in range(n-addnum, n))
			memo.append(ans)
			return ans
	return fibber

>>> fibo = fiblike([1,1])
>>> [fibo(i) for i in range(10)]
[1, 1, 2, 3, 5, 8, 13, 21, 34, 55]
>>> lucas = fiblike([2,1])
>>> [lucas(i) for i in range(10)]
[2, 1, 3, 4, 7, 11, 18, 29, 47, 76]
>>> for n, name in zip(range(2,11), 'fibo tribo tetra penta hexa hepta octo nona deca'.split()) :
	fibber = fiblike([1] + [2**i for i in range(n-1)])
	print('n=%2i, %5snacci -> %s ...' % (n, name, ' '.join(str(fibber(i)) for i in range(15))))

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