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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A349910 A168111 A309491 * A199783 A329645 A318772
KEYWORD
easy,nonn,tabf
AUTHOR
Benjamin de Bivort (bivort(AT)fas.harvard.edu), Aug 04 2005
STATUS
approved

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)