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

0,4

Comments

See A092481 for the definition of isotemporal class. A109622 is the sum of rows.

References

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

Links

Table of n, a(n) for n=0..76.

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)

Example

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.

Crossrefs

Cf. A092481, A109622.

Sequence in context: A349910 A168111 A309491 * A199783 A329645 A318772

Adjacent sequences: A109643 A109644 A109645 * A109647 A109648 A109649

Keyword

easy,nonn,tabf

Author

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

Status

approved