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.

Showing 1-3 of 3 results.

A372705 Number of connected spanning subgraphs of the n-dimensional hypercube graph.

Original entry on oeis.org

1, 1, 5, 1083, 1239326145
Offset: 0

Views

Author

Pontus von Brömssen, May 11 2024

Keywords

Comments

a(n)/A061301(n) is the probability that the n-dimensional hypercube graph is still connected after each edge has been independently deleted with probability 1/2.

Crossrefs

Cf. A006237, A061301, A290758, A359992, A373034, A373035.

A373037 Number of edge subsets E of the n X n square grid graph such that E contains a path between the top left node and the bottom right node.

Original entry on oeis.org

1, 7, 1135, 3329245, 167176484530, 140386491543732211, 1946586793700869420041631, 442196286688432698682908745730140, 1637130627941780284200104764061689410361366, 98421463469915727265279069074012296351284158838933045, 95824439185976594319538143712857075522828165117771969008567719465
Offset: 1

Views

Author

Pontus von Brömssen, May 20 2024

Keywords

Comments

a(n)/A053765(n) is the probability that the top left and bottom right vertices of the n X n square grid graph are still connected after each edge has been independently deleted with probability 1/2.

Links

Crossrefs

Main diagonal of A373036.
Cf. A053765, A373035.

Extensions

a(11) onwards from Eugene Nonko, Oct 28 2024

A373034 Triangle read by rows: T(n,k) is the number of edge subsets E of the n-dimensional hypercube graph such that E contains a path between two given nodes at Hamming distance k, 0 <= k <= n.

Original entry on oeis.org

1, 2, 1, 16, 9, 7, 4096, 2703, 2334, 2160, 4294967296, 3425712321, 3245350248, 3170502909, 3127853061
Offset: 0

Views

Author

Pontus von Brömssen, May 20 2024

Keywords

Comments

T(n,k)/A061301(n) is the probability that two given nodes at Hamming distance k in the n-dimensional hypercube graph are still connected after each edge has been independently deleted with probability 1/2.
The bunkbed conjecture (the version where all edges, including the posts, have the same probability 1/2 of being retained) holds for the n-dimensional hypercube graph if and only if the (n+1)-st row is nonincreasing.

Examples

			Triangle begins:
           1;
           2,          1;
          16,          9,          7;
        4096,       2703,       2334,       2160;
  4294967296, 3425712321, 3245350248, 3170502909, 3127853061;
  ...

Links

Crossrefs

Cf. A061301 (first column), A372705, A373035 (main diagonal).
Showing 1-3 of 3 results.

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

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