A109622 Number of different isotemporal classes of diasters with n peripheral edges.

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

Author

Benjamin de Bivort (bivort(AT)fas.harvard.edu), Aug 02 2005

Keywords

• nonn
• easy

Comments

See A092481 for the definition of isotemporal classes.

Examples

			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.
		

References

• Benjamin de Bivort, Isotemporal classes of diasters, beachballs and daisies, preprint, 2005.

Crossrefs

Cf. A092481, A005993.

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

Extensions

More terms from Sean A. Irvine, Feb 12 2012