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A109646
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Triangle, read by rows, of the number of different isotemporal classes of rotationally distinct diasters with n (rows) total peripheral edges with k (columns) peripheral edges on one side.
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0
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1, 1, 1, 3, 1, 6, 1, 8, 6, 1, 10, 12, 1, 12, 15, 10, 1, 14, 18, 20, 1, 16, 21, 24, 15, 1, 18, 24, 28, 30, 1, 20, 27, 32, 35, 21, 1, 22, 30, 36, 40, 42, 1, 24, 33, 40, 45, 48, 28, 1, 26, 36, 44, 50, 54, 56, 1, 28, 39, 48, 55, 60, 63, 36, 1, 30, 42, 52, 60, 66, 70, 72, 1, 32, 45, 56, 65
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OFFSET
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0,4
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COMMENTS
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See A092481 for the definition of isotemporal class. A109622 is the sum of rows.
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REFERENCES
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B. de Bivort. Isotemporal classes of diasters, beachballs and daisies. Preprint, 2005.
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LINKS
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FORMULA
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for k=0, a(n, k)=1 for k>0 and n!=k, a(n, k)=(n-k)k+(n-k)+k+1 for k>0 and n=k, a(n, k)=(1/2)(k^2+3k+2)
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EXAMPLE
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Row 0 has 1 element, a diaster with no peripheral edges - a singleton edge - for which there is only a single isotemporal class. Row 1 has 1 element, the diaster with a single peripheral edge - two edges sharing a single vertex - for which there is a single isotemporal class. Row 2 has 2 elements, corresponding to the diaster with a two peripheral edges on a single side and the diaster with a single peripheral edge on either side, with 1 and 3 isotemporal classes respectively.
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CROSSREFS
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KEYWORD
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easy,nonn,tabf
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AUTHOR
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Benjamin de Bivort (bivort(AT)fas.harvard.edu), Aug 04 2005
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STATUS
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approved
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