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In words, the sequence of Pell numbers starts with 0 and 1, and then each Pell number is the sum of twice the previous Pell number, plus the Pell number before that. The first few terms of the sequence are 0, 1, 2, 5, 12, 29, 70, 169, 408, 985, 2378, 5741, 13860, … (sequence A000129 in the OEIS).
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 ).
For example, the sequential model of the indexed loop is usually represented as a table of cells, with similar formulas (normally differing only in which cells they reference). Spreadsheets have evolved to use scripting programming languages like VBA as a tool for extensibility beyond what the spreadsheet language makes easy.
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 ...
PKG – format used by Bungie for the PC Beta of Destiny 2, for nearly all the game's assets. CHR – format used by Team Salvato, for the character files of Doki Doki Literature Club! Z5 – format used by Z-machine for story files in interactive fiction. scworld – format used by Survivalcraft to store sandbox worlds.
If () is the generating function of the sequence of Betti numbers () of a space Z, then p X × Y ( t ) = p X ( t ) p Y ( t ) . {\displaystyle p_{X\times Y}(t)=p_{X}(t)p_{Y}(t).} Here when there are finitely many Betti numbers of X and Y , each of which is a natural number rather than ∞ {\displaystyle \infty } , this reads as an identity on ...
The Whittaker–Shannon interpolation formula or sinc interpolation is a method to construct a continuous-time bandlimited function from a sequence of real numbers. The formula dates back to the works of E. Borel in 1898, and E. T. Whittaker in 1915, and was cited from works of J. M. Whittaker in 1935, and in the formulation of the Nyquist–Shannon sampling theorem by Claude Shannon in 1949.
In numerical analysis, Aitken's delta-squared process or Aitken extrapolation is a series acceleration method used for accelerating the rate of convergence of a sequence. It is named after Alexander Aitken, who introduced this method in 1926. [1] It is most useful for accelerating the convergence of a sequence that is converging linearly.