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  2. List of integer sequences - Wikipedia

    en.wikipedia.org/wiki/List_of_integer_sequences

    Recamán's sequence: 0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, ... "subtract if possible, otherwise add": a(0) = 0; for n > 0, a(n) = a(n − 1) − n if that number is positive and not already in the sequence, otherwise a(n) = a(n − 1) + n, whether or not that number is already in the sequence. A005132: Look-and ...

  3. pandas (software) - Wikipedia

    en.wikipedia.org/wiki/Pandas_(software)

    Pandas is built around data structures called Series and DataFrames. Data for these collections can be imported from various file formats such as comma-separated values, JSON, Parquet, SQL database tables or queries, and Microsoft Excel. [8] A Series is a 1-dimensional data structure built on top of NumPy's array.

  4. Constant-recursive sequence - Wikipedia

    en.wikipedia.org/wiki/Constant-recursive_sequence

    A sequence obeying the order-d equation also obeys all higher order equations. These identities may be proved in a number of ways, including via the theory of finite differences. [9] Any sequence of + integer, real, or complex values can be used as initial conditions for a constant-recursive sequence of order +.

  5. Comparison of programming languages (syntax) - Wikipedia

    en.wikipedia.org/wiki/Comparison_of_programming...

    The enclosed text becomes a string literal, which Python usually ignores (except when it is the first statement in the body of a module, class or function; see docstring). Elixir. The above trick used in Python also works in Elixir, but the compiler will throw a warning if it spots this.

  6. List of mathematical series - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_series

    An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.

  7. Generating function - Wikipedia

    en.wikipedia.org/wiki/Generating_function

    A negative-order reversal of this sequence powers formula corresponding to the operation of repeated integration is defined by the zeta series transformation and its generalizations defined as a derivative-based transformation of generating functions, or alternately termwise by and performing an integral transformation on the sequence ...

  8. Arithmetic progression - Wikipedia

    en.wikipedia.org/wiki/Arithmetic_progression

    Proof without words of the arithmetic progression formulas using a rotated copy of the blocks. An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that ...

  9. Formulas for generating Pythagorean triples - Wikipedia

    en.wikipedia.org/wiki/Formulas_for_generating...

    Michael Stifel published the following method in 1544. [3] [4] Consider the sequence of mixed numbers,,,, … with = + +.To calculate a Pythagorean triple, take any term of this sequence and convert it to an improper fraction (for mixed number , the corresponding improper fraction is ).