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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.
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 ...
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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.
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).
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 ...
I don't know if "lazy caterer's sequence" is the best name for this article. It is the second name given in the OEIS, the first being "central polygonal numbers." Anton Mravcek 21:43, 14 Jun 2005 (UTC) The only thing I have against the term "central polygonal number" is that is could easily be confused with centered number.