Sets of nested wooden boxes or traditional nested Russian dolls come to mind here. (This application of the sequence was inspired by considering leftover moving boxes.) If the restriction exists that each object is able or permitted to contain at most one smaller (but possibly nested) object at a time, the resulting sequence begins 1,2,5,15,52 (Bell Numbers?). Arbitrary levels of nesting of objects are permitted within arrangements. Given n objects of distinct sizes (e.g., areas, volumes) such that each object is sufficiently large to simultaneously contain all previous objects, then n! is the total number of essentially different arrangements using all n objects. Amarnath Murthy, Jul 01 2003Ī(n) is the permanent of the n X n matrix M with M(i, j) = 1. N! is the smallest number with that prime signature. , n - 1 elements X (e.g., at n = 5, we consider the distinct subsets of ABBCCCDDDD and there are 5! = 120). Number of distinct subsets of T(n-1) elements with 1 element A, 2 elements B. This sequence is the BinomialMean transform of A000354. Sloane, Apr 07 2014įor n >= 1, a(n) is the number of n X n (0,1) matrices with each row and column containing exactly one entry equal to 1. (See Knuth, also the Zeilberger link) - N. The earliest publication that discusses this sequence appears to be the Sepher Yezirah, circa AD 300.
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