A109646 Triangle, read by rows, of the number of different isotemporal classes of rotationally distinct diasters with n (rows) total peripheral edges with k (columns) peripheral edges on one side.

1, 1, 1, 3, 1, 6, 1, 8, 6, 1, 10, 12, 1, 12, 15, 10, 1, 14, 18, 20, 1, 16, 21, 24, 15, 1, 18, 24, 28, 30, 1, 20, 27, 32, 35, 21, 1, 22, 30, 36, 40, 42, 1, 24, 33, 40, 45, 48, 28, 1, 26, 36, 44, 50, 54, 56, 1, 28, 39, 48, 55, 60, 63, 36, 1, 30, 42, 52, 60, 66, 70, 72, 1, 32, 45, 56, 65

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 rows.

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 1 element, the diaster with a single peripheral edge - two edges sharing a single vertex - for which there is a single isotemporal class. Row 2 has 2 elements, corresponding to the diaster with a two peripheral edges on a single side and the diaster with a single peripheral edge on either side, with 1 and 3 isotemporal classes respectively.
		

References

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

Crossrefs

Cf. A092481, A109622.

Formula

for k=0, a(n, k)=1 for k>0 and n!=k, a(n, k)=(n-k)k+(n-k)+k+1 for k>0 and n=k, a(n, k)=(1/2)(k^2+3k+2)