A109647 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.

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

Offset: 0

Author

Benjamin de Bivort (bivort(AT)fas.harvard.edu), Aug 04 2005

Keywords

• easy
• nonn
• tabf

Comments

See A092481 for the definition of isotemporal class. A109622 is the sum of elements 1, 2,.., floor(n/2) for each row.

Examples

			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.
		

References

• B. de Bivort. Isotemporal classes of diasters, beachballs and daisies. Preprint, 2005.

Crossrefs

Cf. A092481, A109622.

Formula

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