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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

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

Keywords

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

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.

Original entry on oeis.org

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

Views

Author

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

Keywords

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)

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.

Original entry on oeis.org

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

Views

Author

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

Keywords

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
Showing 1-3 of 3 results.

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