A360846 -id:A360846 - cp's OEIS frontend

A360847 Number of dominating induced trees in the n X n grid graph.

1, 8, 65, 1280, 78981, 14605388, 7904828158, 12456744197696, 57118103869618858, 760896261783236975004, 29416443122724544970455433, 3297715940113139272931793598648, 1071333966021766251746119497973623975, 1008129126269380724757869194465038817386728

Offset: 1

Andrew Howroyd, Feb 23 2023

nonn

A dominating induced tree in a graph is an acyclic connected induced subgraph whose vertices are a dominating set.

Eric Weisstein's World of Mathematics, Grid Graph.

Main diagonal of A360846.

Cf. A287690 (connected dominating sets), A360203 (induced trees).

A360848 Number of dominating induced trees in the n-ladder graph P_2_X P_n.

Original entry on oeis.org

3, 8, 17, 32, 66, 130, 262, 522, 1046, 2090, 4182, 8362, 16726, 33450, 66902, 133802, 267606, 535210, 1070422, 2140842, 4281686, 8563370, 17126742, 34253482, 68506966, 137013930, 274027862, 548055722, 1096111446, 2192222890, 4384445782, 8768891562

Offset: 1

Andrew Howroyd, Feb 23 2023

Andrew Howroyd, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Ladder Graph.
Index entries for linear recurrences with constant coefficients, signature (1,2).

Row 2 of A360846.

LinearRecurrence[{1, 2}, {3, 8, 17, 32}, 50] (* Paolo Xausa, Oct 03 2024 *)

Vec((3 + 5*x + 3*x^2 - x^3)/((1 + x)*(1 - 2*x)) + O(x^20))

a(n) = a(n-1) + 2*a(n-2) for n > 4.

G.f.: x*(3 + 5*x + 3*x^2 - x^3)/((1 + x)*(1 - 2*x)).

cp's OEIS Frontend

A360847 Number of dominating induced trees in the n X n grid graph.

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A360848 Number of dominating induced trees in the n-ladder graph P_2_X P_n.

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