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Suppose one wants to determine the 5-combination at position 72. The successive values of () for n = 4, 5, 6, ... are 0, 1, 6, 21, 56, 126, 252, ..., of which the largest one not exceeding 72 is 56, for n = 8. Therefore c 5 = 8, and the remaining elements form the 4-combination at position 72 − 56 = 16.
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.
The numbers of compositions of n +1 into k +1 ordered partitions form Pascal's triangle Using the Fibonacci sequence to count the {1, 2}-restricted compositions of n, for example, the number of ways one can ascend a staircase of length n, taking one or two steps at a time
For example, if you had two types of coins valued at 6 cents and 14 cents, the GCD would equal 2, and there would be no way to combine any number of such coins to produce a sum which was an odd number; additionally, even numbers 2, 4, 8, 10, 16 and 22 (less than m=24) could not be formed, either.
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
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By contrast the encodings considered here choose the first number from a set of n values, the next number from a fixed set of n − 1 values, and so forth decreasing the number of possibilities until the last number for which only a single fixed value is allowed; every sequence of numbers chosen from these sets encodes a single permutation.
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