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A185634
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Number of n-length cycles from any point in a complete graph on n nodes.
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1
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1, 2, 21, 204, 2605, 39990, 720601, 14913080, 348678441, 9090909090, 261535698061, 8230246567620, 281241170407093, 10371206370520814, 410525522232055665, 17361641481138401520, 781282469559318055057, 37275544492386193492506, 1879498672877297909667781
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OFFSET
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2,2
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COMMENTS
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If M is the n X n matrix filled with ones, a(n) is the upper left element of (M-Id)^n
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LINKS
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FORMULA
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a(n) = floor((n-1)^n/n) + ((-1)^n+1)/2
a(n) = floor((n-1)^n/n)+1 for n odd, a(n) = floor((n-1)^n/n) for n even.
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EXAMPLE
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In a complete graph in 5 nodes, there are 204 different cycles with a length of 5, from a point to itself.
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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