A360202 - OEIS

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.

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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..435

Eric Weisstein's World of Mathematics, Grid Graph.

Eric Weisstein's World of Mathematics, Induced Subgraph.

FORMULA

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

EXAMPLE

Array begins:

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

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.

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

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

Sequence in context: A367644 A094305 A360850 * A057963 A250301 A261954

Adjacent sequences: A360199 A360200 A360201 * A360203 A360204 A360205

KEYWORD

nonn,tabl

AUTHOR

Andrew Howroyd, Feb 22 2023

STATUS

approved