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  2. Padovan sequence - Wikipedia

    en.wikipedia.org/wiki/Padovan_sequence

    P(n) is the number of ways of writing n + 2 as an ordered sum in which each term is either 2 or 3 (i.e. the number of compositions of n + 2 in which each term is either 2 or 3). For example, P(6) = 4, and there are 4 ways to write 8 as an ordered sum of 2s and 3s:

  3. Fibonacci sequence - Wikipedia

    en.wikipedia.org/wiki/Fibonacci_sequence

    This sequence of numbers of parents is the Fibonacci sequence. The number of ancestors at each level, F n, is the number of female ancestors, which is F n−1, plus the number of male ancestors, which is F n−2. [91] [92] This is under the unrealistic assumption that the ancestors at each level are otherwise unrelated.

  4. Look-and-say sequence - Wikipedia

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

    This variation ultimately ends up repeating the number 21322314 ("two 1s, three 2s, two 3s and one 4"). These sequences differ in several notable ways from the look-and-say sequence. Notably, unlike the Conway sequences, a given term of the pea pattern does not uniquely define the preceding term.

  5. Pell number - Wikipedia

    en.wikipedia.org/wiki/Pell_number

    In words: the first two numbers in the sequence are both 2, and each successive number is formed by adding twice the previous Pell–Lucas number to the Pell–Lucas number before that, or equivalently, by adding the next Pell number to the previous Pell number: thus, 82 is the companion to 29, and 82 = 2 × 34 + 14 = 70 + 12.

  6. Geometric progression - Wikipedia

    en.wikipedia.org/wiki/Geometric_progression

    Diagram illustrating three basic geometric sequences of the pattern 1(r n−1) up to 6 iterations deep.The first block is a unit block and the dashed line represents the infinite sum of the sequence, a number that it will forever approach but never touch: 2, 3/2, and 4/3 respectively.

  7. Hexagonal number - Wikipedia

    en.wikipedia.org/wiki/Hexagonal_number

    Proof without words that a hexagonal number (middle column) can be rearranged as rectangular and odd-sided triangular numbers. A hexagonal number is a figurate number.The nth hexagonal number h n is the number of distinct dots in a pattern of dots consisting of the outlines of regular hexagons with sides up to n dots, when the hexagons are overlaid so that they share one vertex.

  8. Generalizations of Fibonacci numbers - Wikipedia

    en.wikipedia.org/wiki/Generalizations_of...

    A repfigit, or Keith number, is an integer such that, when its digits start a Fibonacci sequence with that number of digits, the original number is eventually reached. An example is 47, because the Fibonacci sequence starting with 4 and 7 (4, 7, 11, 18, 29, 47) reaches 47.

  9. List of integer sequences - Wikipedia

    en.wikipedia.org/wiki/List_of_integer_sequences

    A number that has the same number of digits as the number of digits in its prime factorization, including exponents but excluding exponents equal to 1. A046758: Extravagant numbers: 4, 6, 8, 9, 12, 18, 20, 22, 24, 26, 28, 30, 33, 34, 36, 38, ... A number that has fewer digits than the number of digits in its prime factorization (including ...