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Search: id:A109647
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| A109647 |
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Triangle, read by rows, of the number of different isotemporal classes of diasters with n (row) total peripheral edges with k (column) peripheral edges on the a given side. |
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+0
1
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| 1, 1, 1, 1, 3, 1, 1, 6, 6, 1, 1, 8, 6, 8, 1, 1, 10, 12, 12, 10, 1, 1, 12, 15, 10, 15, 12, 1, 1, 14, 18, 20, 20, 18, 14, 1, 1, 16, 21, 24, 15, 24, 21, 16, 1, 1, 18, 24, 28, 30, 30, 28, 24, 18, 1, 1, 20, 27, 32, 35, 21, 35, 32, 27, 20, 1, 1, 22, 30, 36, 40, 42, 42, 40, 36, 30, 22, 1, 1, 24
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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See A092481 for the definition of isotemporal class. A109622 is the sum of elements 1, 2,.., floor(n/2) for each row.
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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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FORMULA
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if k=0|n a(n, k)=1 if k=n/2 a(n, k)=(1/2)(k^2+3k+2) else a(n, k)=(n-k)k+(n-k)+k+1
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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 2 elements, the diaster with a single peripheral edge on the left, and the diaster with the single peripheral edge on the right - two edges sharing a single vertex - for each, there is a single isotemporal class. Row 2 has 3 elements, corresponding to the diaster with a two peripheral edges on the left, the diaster with a single peripheral edge on either side, and the diaster with both peripheral edges on the right. These graphs have 1, 3, and 1 isotemporal classes respectively.
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CROSSREFS
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Cf. A092481, A109622.
Sequence in context: A129818 A055898 A035582 this_sequence A054120 A114176 A056241
Adjacent sequences: A109644 A109645 A109646 this_sequence A109648 A109649 A109650
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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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