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Revision History for A360202

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A360202

Array read by antidiagonals: T(m,n) is the number of (non-null) induced trees in the grid graph P_m X P_n.
(history; published version)

#11 by Michael De Vlieger at Mon Feb 27 20:29:52 EST 2023

STATUS

proposed

approved

#10 by Andrew Howroyd at Mon Feb 27 19:38:45 EST 2023

STATUS

editing

proposed

#9 by Andrew Howroyd at Mon Feb 27 19:38:28 EST 2023

LINKS

Andrew Howroyd, <a href="/A360202/b360202.txt">Table of n, a(n) for n = 1..435</a>

#8 by Andrew Howroyd at Mon Feb 27 19:16:48 EST 2023

FORMULA

T(m,n) = T(n,m).

#7 by Andrew Howroyd at Mon Feb 27 19:16:25 EST 2023

LINKS

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>.

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/InducedSubgraph.html">Induced Subgraph</a>.

EXAMPLE

Table startsArray begins:

CROSSREFS

Cf. A287151 (connected induced subgraphs), A116469 (spanning trees), A360196 (induced cycles), A360199 (induced paths), A360918 (maximum induced trees).

STATUS

approved

editing

#6 by Michael De Vlieger at Wed Feb 22 21:42:49 EST 2023

STATUS

proposed

approved

#5 by Andrew Howroyd at Wed Feb 22 20:09:02 EST 2023

STATUS

editing

proposed

#4 by Andrew Howroyd at Wed Feb 22 19:52:15 EST 2023

CROSSREFS

Cf. A287151 (connected induced subgraphs), A116469 (spanning trees), A360196 (induced cycles), A360199 (induced paths).

#3 by Andrew Howroyd at Wed Feb 22 19:35:55 EST 2023

CROSSREFS

Row Rows 1 is ..2 are A000217, 3*A125128.

#2 by Andrew Howroyd at Wed Feb 22 19:30:58 EST 2023

NAME

allocated for Andrew HowroydArray read by antidiagonals: T(m,n) is the number of (non-null) induced trees in the grid graph P_m X P_n.

DATA

1, 3, 3, 6, 12, 6, 10, 33, 33, 10, 15, 78, 138, 78, 15, 21, 171, 533, 533, 171, 21, 28, 360, 2003, 3568, 2003, 360, 28, 36, 741, 7453, 23686, 23686, 7453, 741, 36, 45, 1506, 27643, 156614, 277606, 156614, 27643, 1506, 45, 55, 3039, 102432, 1034875, 3234373, 3234373, 1034875, 102432, 3039, 55

OFFSET

1,2

LINKS

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/InducedSubgraph.html">Induced Subgraph</a>

EXAMPLE

Table starts:

=============================================================

m\n| 1 2 3 4 5 6 7 ...

---+---------------------------------------------------------

1 | 1 3 6 10 15 21 28 ...

2 | 3 12 33 78 171 360 741 ...

3 | 6 33 138 533 2003 7453 27643 ...

4 | 10 78 533 3568 23686 156614 1034875 ...

5 | 15 171 2003 23686 277606 3234373 37643572 ...

6 | 21 360 7453 156614 3234373 66136452 1349087217 ...

7 | 28 741 27643 1034875 37643572 1349087217 48136454388 ...

...

CROSSREFS

Main diagonal is A360203.

Row 1 is A000217.

Cf. A287151 (connected induced subgraphs), A360196 (induced cycles), A360199 (induced paths).

KEYWORD

allocated

nonn,tabl

AUTHOR

Andrew Howroyd, Feb 22 2023

STATUS

approved

editing