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The maximum number of pieces, p obtainable with n straight cuts is the n-th triangular number plus one, forming the lazy caterer's sequence (OEIS A000124) The maximum number p of pieces that can be created with a given number of cuts n (where n ≥ 0) is given by the formula
The maximum number of pieces, p obtainable with n straight cuts is the n-th triangular number plus one, forming the lazy caterer's sequence (OEIS A000124) One way of calculating the depreciation of an asset is the sum-of-years' digits method, which involves finding T n, where n is the length in years of the asset's useful life.
The cake numbers are the 3-dimensional analogue of the 2-dimensional lazy caterer's sequence. The difference between successive cake numbers also gives the lazy caterer's sequence. [1] Cake numbers (blue) and other OEIS sequences in Bernoulli's triangle. The fourth column of Bernoulli's triangle (k = 3) gives the cake numbers for n cuts, where ...
As the third column of Bernoulli's triangle (k = 2) is a triangular number plus one, it forms the lazy caterer's sequence for n cuts, where n ≥ 2. [4] The fourth column (k = 3) is the three-dimensional analogue, known as the cake numbers, for n cuts, where n ≥ 3. [5]
The numbers along the left edge of the triangle are the lazy caterer's sequence and the numbers along the right edge are the triangular numbers. The nth row sums to n(n 2 + 1)/2, the constant of an n × n magic square (sequence A006003 in the OEIS).
This sequence is dominating, but none of its circular shifts , , and are. A string is a Dyck word of n {\displaystyle n} X's and n {\displaystyle n} Y's if and only if prepending an X to the Dyck word gives a dominating sequence with n + 1 {\displaystyle n+1} X's and n {\displaystyle n} Y's, so we can count the former by instead counting the ...
The number of points (n), chords (c) and regions (r G) for first 6 terms of Moser's circle problem. In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser's circle problem (named after Leo Moser), has a solution by an inductive method.
Sequences of weight distribution codes often omit periodically recurring zeros. For example, consider: the prime numbers, the palindromic primes, the Fibonacci sequence, the lazy caterer's sequence, and the coefficients in the series expansion of (+) (). In OEIS lexicographic order, they are: