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.

A297664 Number of chordless cycles in the n X n grid graph.

Original entry on oeis.org

0, 1, 5, 24, 229, 3436, 65772, 1743247, 78586742, 7234839185, 1330059590925, 421587920205546, 212201572752086670, 170288846375423693683, 227570453486998336648738, 527014715702923506908210573, 2140337449056844246626590305042, 15055309813180236733267168372538873
Offset: 1

Views

Author

Eric W. Weisstein, Jan 02 2018

Keywords

Links

Crossrefs

Main diagonal of A360196.
Cf. A003763, A140517, A360200, A360914.

Extensions

a(7)-a(18) from Andrew Howroyd, Jan 08 2018

A360199 Array read by antidiagonals: T(m,n) is the number of induced paths in the grid graph P_m X P_n.

Original entry on oeis.org

0, 1, 1, 3, 8, 3, 6, 25, 25, 6, 10, 58, 94, 58, 10, 15, 117, 270, 270, 117, 15, 21, 218, 681, 1004, 681, 218, 21, 28, 387, 1597, 3330, 3330, 1597, 387, 28, 36, 666, 3592, 10224, 14864, 10224, 3592, 666, 36, 45, 1123, 7880, 29924, 61165, 61165, 29924, 7880, 1123, 45
Offset: 1

Views

Author

Andrew Howroyd, Jan 29 2023

Keywords

Comments

Paths of length zero are not counted here.

Examples

			Array begins:
============================================================
m\n|  1   2    3     4      5       6        7         8 ...
---+--------------------------------------------------------
1  |  0   1    3     6     10      15       21        28 ...
2  |  1   8   25    58    117     218      387       666 ...
3  |  3  25   94   270    681    1597     3592      7880 ...
4  |  6  58  270  1004   3330   10224    29924     85036 ...
5  | 10 117  681  3330  14864   61165   238897    907148 ...
6  | 15 218 1597 10224  61165  334536  1723535   8647932 ...
7  | 21 387 3592 29924 238897 1723535 11546874  75134416 ...
8  | 28 666 7880 85036 907148 8647932 75134416 629381852 ...
   ...

Links

Crossrefs

Main diagonal is A360200.
Rows 1..2 are A000217(n-1), A360201.
Cf. A287151 (induced connected subgraphs), A288518 (undirected paths), A360196 (induced cycles), A360202 (induced trees), A360916 (maximum induced paths).

A360203 Number of (non-null) induced trees in the n X n grid graph.

Original entry on oeis.org

1, 12, 138, 3568, 277606, 66136452, 48136454388, 106601739449932, 716581962133166734, 14594259085593605592840, 899530518959027898354960664, 167638624754374503965030664785872, 94397539071875018677962029008899452442, 160524233982090828046095750880433748533447560
Offset: 1

Views

Author

Andrew Howroyd, Feb 22 2023

Keywords

Links

Crossrefs

Main diagonal of A360202.
Cf. A059525, A080691, A297664, A360200.
Showing 1-3 of 3 results.

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

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