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Search: id:A109622
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| A109622 |
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Number of different isotemporal classes of diasters with n peripheral edges. |
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+0
3
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| 1, 1, 4, 7, 15, 23, 38, 53, 77, 101, 136, 171, 219, 267, 330, 393, 473, 553, 652, 751, 871, 991, 1134, 1277, 1445, 1613, 1808, 2003, 2227, 2451, 2706, 2961, 3249, 3537, 3860, 4183, 4543, 4903, 5302, 5701, 6141
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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See A092481 for the definition of isotemporal classes.
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REFERENCES
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Benjamin de Bivort, Isotemporal classes of diasters, beachballs, and daisies, preprint, 2005.
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FORMULA
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a(n=2k) = 1 + sum_{i=1}^{(n/2)-1} ((n-i)i+n+i+1) + (1/2)((n/2)^2+3(n/2)+2) a(n=2k+1)= 1 + sum_{i=1}^{(n-1)/2} ((n-i)i+n+i+1)
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EXAMPLE
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A diaster is defined to be any graph with a central edge with vertices of degree j and k, and j+k peripheral edges connected to the central edge each terminating in a vertex of degree 1. a(5)=23 refers to diasters with 5 peripheral edges. These can be uniquely arranged with 0, 1 or 2 peripheral edges on a particular side, yielding 1, 10 and 12 isotemporal classes respectively each.
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CROSSREFS
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Cf. A092481.
Adjacent sequences: A109619 A109620 A109621 this_sequence A109623 A109624 A109625
Sequence in context: A049832 A092309 A039669 this_sequence A124286 A027419 A116969
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KEYWORD
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easy,nonn
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AUTHOR
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Benjamin de Bivort (bivort(AT)fas.harvard.edu), Aug 02 2005
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