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A109622
Number of different isotemporal classes of diasters with n peripheral edges.
2
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, 6581, 7064, 7547, 8075, 8603
OFFSET
0,3
COMMENTS
See A092481 for the definition of isotemporal classes.
REFERENCES
Benjamin de Bivort, Isotemporal classes of diasters, beachballs and daisies, preprint, 2005.
FORMULA
a(n=2k) = 1 + sum_{i=1}^{(n/2)-1} (n*i-i^2+n+1) + (1/2)((n/2)^2+3(n/2)+2) a(n=2k+1)= 1 + sum_{i=1}^{(n-1)/2} ((n*i-i^2+n+1). [Corrected by Sean A. Irvine after private communication with Benjamin de Bivort, Feb 13 2012]
a(n) = A005993(n) - n. - Enrique Pérez Herrero, Apr 22 2012
EXAMPLE
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.
CROSSREFS
Sequence in context: A271675 A356714 A039669 * A269967 A124286 A235603
KEYWORD
nonn,easy
AUTHOR
Benjamin de Bivort (bivort(AT)fas.harvard.edu), Aug 02 2005
EXTENSIONS
More terms from Sean A. Irvine, Feb 12 2012
STATUS
approved