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  2. List of integer sequences - Wikipedia

    en.wikipedia.org/wiki/List_of_integer_sequences

    Name First elements Short description OEIS Kolakoski sequence: 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, ... The n th term describes the length of the n th run : A000002: Euler's ...

  3. Padovan sequence - Wikipedia

    en.wikipedia.org/wiki/Padovan_sequence

    6 ; 3 + 3 ; 1 + 4 + 1 ; 1 + 1 + 1 + 1 + 1 + 1. The number of ways of writing n as an ordered sum in which each term is odd and greater than 1 is equal to P(n − 5). For example, P(6) = 4, and there are 4 ways to write 11 as an ordered sum in which each term is odd and greater than 1: 11 ; 5 + 3 + 3 ; 3 + 5 + 3 ; 3 + 3 + 5. The number of ways ...

  4. Look-and-say sequence - Wikipedia

    en.wikipedia.org/wiki/Look-and-say_sequence

    1 is read off as "one 1" or 11. 11 is read off as "two 1s" or 21. 21 is read off as "one 2, one 1" or 1211. 1211 is read off as "one 1, one 2, two 1s" or 111221. 111221 is read off as "three 1s, two 2s, one 1" or 312211. The look-and-say sequence was analyzed by John Conway [1] after he was introduced to it by one of his students at a party. [2 ...

  5. Fibonacci sequence - Wikipedia

    en.wikipedia.org/wiki/Fibonacci_sequence

    A bijection with the sums to n is to replace 1 with 0 and 2 with 11. The number of binary strings of length n without an even number of consecutive 0 s or 1 s is 2F n. For example, out of the 16 binary strings of length 4, there are 2F 4 = 6 without an even number of consecutive 0 s or 1 s—they are 0001, 0111, 0101, 1000, 1010, 1110. There is ...

  6. Lazy caterer's sequence - Wikipedia

    en.wikipedia.org/wiki/Lazy_caterer's_sequence

    The maximum number of pieces from consecutive cuts are the numbers in the Lazy Caterer's Sequence. When a circle is cut n times to produce the maximum number of pieces, represented as p = f (n), the n th cut must be considered; the number of pieces before the last cut is f (n − 1), while the number of pieces added by the last cut is n.

  7. On-Line Encyclopedia of Integer Sequences - Wikipedia

    en.wikipedia.org/wiki/On-Line_Encyclopedia_of...

    The On-Line Encyclopedia of Integer Sequences (OEIS) is an online database of integer sequences.It was created and maintained by Neil Sloane while researching at AT&T Labs.