cp's OEIS Frontend

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.

Previous Showing 71-80 of 6133 results. Next

A315615 Coordination sequence Gal.6.609.6 where Gal.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.

Original entry on oeis.org

1, 6, 12, 15, 18, 21, 24, 33, 42, 45, 48, 51, 54, 57, 60, 72, 84, 84, 84, 87, 90, 93, 96, 111, 126, 123, 120, 123, 126, 129, 132, 150, 168, 162, 156, 159, 162, 165, 168, 189, 210, 201, 192, 195, 198, 201, 204, 228, 252, 240
Offset: 0

Views

Author

Brian Galebach and N. J. A. Sloane, Jun 18 2018

Keywords

Comments

Note that there may be other vertices in the Galebach list of u-uniform tilings with u <= 6 that have this same coordination sequence. See the Galebach link for the complete list of A-numbers for all these tilings.

Links

Formula

From Chai Wah Wu, Dec 20 2019: (Start)
a(n) = 2*a(n-1) - 3*a(n-2) + 4*a(n-3) - 5*a(n-4) + 6*a(n-5) - 7*a(n-6) + 8*a(n-7) - 7*a(n-8) + 6*a(n-9) - 5*a(n-10) + 4*a(n-11) - 3*a(n-12) + 2*a(n-13) - a(n-14) for n > 14 (conjectured).
G.f.: (x^14 + 4*x^13 + 3*x^12 + 5*x^11 + 5*x^10 + 6*x^9 + 7*x^8 + 13*x^7 + 7*x^6 + 6*x^5 + 5*x^4 + 5*x^3 + 3*x^2 + 4*x + 1)/((x - 1)^2*(x^2 + 1)^2*(x^4 + 1)^2) (conjectured). (End)

A315907 Coordination sequence Gal.3.40.3 where Gal.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.

Original entry on oeis.org

1, 6, 8, 14, 20, 22, 28, 34, 36, 42, 48, 50, 56, 62, 64, 70, 76, 78, 84, 90, 92, 98, 104, 106, 112, 118, 120, 126, 132, 134, 140, 146, 148, 154, 160, 162, 168, 174, 176, 182, 188, 190, 196, 202, 204, 210, 216, 218, 224, 230
Offset: 0

Views

Author

Brian Galebach and N. J. A. Sloane, Jun 18 2018

Keywords

Comments

Note that there may be other vertices in the Galebach list of u-uniform tilings with u <= 6 that have this same coordination sequence. See the Galebach link for the complete list of A-numbers for all these tilings.

Links

Crossrefs

Cf. A047342.

Formula

Conjectures from R. J. Mathar, May 02 2023: (Start)
G.f.: 1 + 2*x*(3+x+3*x^2) / ( (1+x+x^2)*(x-1)^2 ).
a(n) = a(n-1) + a(n-3) - a(n-4) for n > 4.
a(n) = 2*A047342(n+1) for n > 0. (End)

A316318 Coordination sequence for a node in the graph of Balaban's (3,10)-cage.

Original entry on oeis.org

1, 3, 6, 12, 24, 20, 4
Offset: 0

Views

Author

N. J. A. Sloane, Jul 01 2018

Keywords

Comments

The graph has 70 nodes, 105 edges, degree 3, girth 10 and diameter 6.
The automorphism group of this graph has order 80, and has three orbits on nodes, of sizes 40, 20, and 10, respectively. However, the coordination sequence is independent of the choice of the node.

Links

Crossrefs

See A250120 for links to thousands of other coordination sequences.

A310001 Coordination sequence Gal.6.108.1 where Gal.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.

Original entry on oeis.org

1, 3, 4, 6, 10, 13, 16, 16, 20, 28, 24, 25, 30, 33, 34, 36, 42, 45, 43, 52, 53, 56, 50, 59, 66, 63, 60, 69, 72, 77, 72, 81, 82, 86, 88, 90, 90, 93, 94, 108, 98, 103, 106, 113, 112, 113, 116, 122, 117, 132
Offset: 0

Views

Author

Brian Galebach and N. J. A. Sloane, Jun 18 2018

Keywords

Comments

Note that there may be other vertices in the Galebach list of u-uniform tilings with u <= 6 that have this same coordination sequence. See the Galebach link for the complete list of A-numbers for all these tilings.

Links

A310002 Coordination sequence Gal.5.44.1 where Gal.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.

Original entry on oeis.org

1, 3, 4, 6, 10, 13, 16, 17, 18, 24, 23, 27, 33, 36, 35, 35, 39, 44, 41, 48, 54, 59, 54, 56, 60, 62, 60, 68, 76, 82, 71, 77, 81, 83, 79, 86, 99, 104, 89, 98, 100, 104, 98, 107, 122, 124, 108, 118, 120, 125
Offset: 0

Views

Author

Brian Galebach and N. J. A. Sloane, Jun 18 2018

Keywords

Comments

Note that there may be other vertices in the Galebach list of u-uniform tilings with u <= 6 that have this same coordination sequence. See the Galebach link for the complete list of A-numbers for all these tilings.

Links

A310003 Coordination sequence Gal.5.45.1 where Gal.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.

Original entry on oeis.org

1, 3, 4, 6, 10, 14, 20, 18, 20, 24, 26, 27, 29, 40, 44, 43, 39, 43, 50, 49, 48, 53, 69, 73, 66, 61, 67, 75, 72, 69, 77, 98, 102, 90, 82, 90, 100, 96, 91, 100, 127, 131, 114, 103, 113, 126, 119, 112, 123, 157
Offset: 0

Views

Author

Brian Galebach and N. J. A. Sloane, Jun 18 2018

Keywords

Comments

Note that there may be other vertices in the Galebach list of u-uniform tilings with u <= 6 that have this same coordination sequence. See the Galebach link for the complete list of A-numbers for all these tilings.

Links

A310004 Coordination sequence Gal.6.106.1 where Gal.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.

Original entry on oeis.org

1, 3, 4, 6, 10, 16, 21, 20, 22, 23, 29, 29, 32, 38, 47, 49, 47, 47, 48, 54, 52, 58, 65, 78, 75, 72, 73, 77, 79, 75, 84, 92, 109, 101, 97, 97, 104, 105, 101, 109, 119, 140, 127, 122, 122, 131, 129, 126, 135, 149
Offset: 0

Views

Author

Brian Galebach and N. J. A. Sloane, Jun 18 2018

Keywords

Comments

Note that there may be other vertices in the Galebach list of u-uniform tilings with u <= 6 that have this same coordination sequence. See the Galebach link for the complete list of A-numbers for all these tilings.

Links

A310005 Coordination sequence Gal.6.107.1 where Gal.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.

Original entry on oeis.org

1, 3, 4, 6, 10, 16, 22, 24, 23, 25, 29, 31, 32, 35, 45, 55, 56, 53, 50, 54, 59, 59, 59, 63, 79, 93, 91, 81, 76, 83, 90, 88, 85, 92, 114, 132, 125, 109, 103, 111, 120, 116, 112, 120, 148, 171, 160, 138, 129, 140
Offset: 0

Views

Author

Brian Galebach and N. J. A. Sloane, Jun 18 2018

Keywords

Comments

Note that there may be other vertices in the Galebach list of u-uniform tilings with u <= 6 that have this same coordination sequence. See the Galebach link for the complete list of A-numbers for all these tilings.

Links

A310006 Coordination sequence Gal.4.33.3 where Gal.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.

Original entry on oeis.org

1, 3, 4, 6, 12, 14, 14, 14, 18, 28, 30, 23, 30, 37, 30, 38, 44, 48, 44, 42, 52, 62, 62, 53, 52, 69, 68, 72, 80, 70, 72, 80, 72, 98, 98, 83, 86, 93, 98, 110, 108, 104, 98, 108, 114, 128, 130, 109, 110, 135
Offset: 0

Views

Author

Brian Galebach and N. J. A. Sloane, Jun 18 2018

Keywords

Comments

Note that there may be other vertices in the Galebach list of u-uniform tilings with u <= 6 that have this same coordination sequence. See the Galebach link for the complete list of A-numbers for all these tilings.

Links

A310007 Coordination sequence Gal.4.31.1 where Gal.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.

Original entry on oeis.org

1, 3, 4, 7, 12, 18, 19, 17, 18, 23, 27, 32, 40, 43, 40, 37, 38, 43, 48, 57, 68, 68, 61, 57, 58, 63, 69, 82, 96, 93, 82, 77, 78, 83, 90, 107, 124, 118, 103, 97, 98, 103, 111, 132, 152, 143, 124, 117, 118, 123
Offset: 0

Views

Author

Brian Galebach and N. J. A. Sloane, Jun 18 2018

Keywords

Comments

Note that there may be other vertices in the Galebach list of u-uniform tilings with u <= 6 that have this same coordination sequence. See the Galebach link for the complete list of A-numbers for all these tilings.

Links

Formula

Conjectures from Chai Wah Wu, Dec 10 2018: (Start)
a(n) = 2*a(n-1) - 3*a(n-2) + 4*a(n-3) - 5*a(n-4) + 6*a(n-5) - 7*a(n-6) + 8*a(n-7) - 7*a(n-8) + 6*a(n-9) - 5*a(n-10) + 4*a(n-11) - 3*a(n-12) + 2*a(n-13) - a(n-14) for n > 16.
G.f.: (-2*x^16 + 4*x^15 - 3*x^14 + 5*x^13 - 5*x^12 + 12*x^11 - 3*x^10 + 12*x^9 - 2*x^8 + 9*x^7 + 8*x^5 + 3*x^4 + 4*x^3 + x^2 + x + 1)/((x - 1)^2*(x^2 + 1)^2*(x^4 + 1)^2). (End)
Previous Showing 71-80 of 6133 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.