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 A360846 Array read by antidiagonals: T(m,n) is the number of dominating induced trees in the grid graph P_m X P_n. 3
 1, 3, 3, 4, 8, 4, 4, 17, 17, 4, 4, 32, 65, 32, 4, 4, 66, 222, 222, 66, 4, 4, 130, 766, 1280, 766, 130, 4, 4, 262, 2685, 7629, 7629, 2685, 262, 4, 4, 522, 9450, 46032, 78981, 46032, 9450, 522, 4, 4, 1046, 33158, 278419, 820308, 820308, 278419, 33158, 1046, 4 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A dominating induced tree in a graph is an acyclic connected induced subgraph whose vertices are a dominating set. LINKS Andrew Howroyd, Table of n, a(n) for n = 1..435 (first 29 antidiagonals) Eric Weisstein's World of Mathematics, Grid Graph. FORMULA T(n,m) = T(m,n). EXAMPLE Table starts: ======================================================= m\n| 1 2 3 4 5 6 7 ... ---+--------------------------------------------------- 1 | 1 3 4 4 4 4 4 ... 2 | 3 8 17 32 66 130 262 ... 3 | 4 17 65 222 766 2685 9450 ... 4 | 4 32 222 1280 7629 46032 278419 ... 5 | 4 66 766 7629 78981 820308 8520021 ... 6 | 4 130 2685 46032 820308 14605388 259809527 ... 7 | 4 262 9450 278419 8520021 259809527 7904828158 ... ... CROSSREFS Main diagonal is A360847. Rows 1..2 are A113311(n-1), A360848. Cf. A291872 (connected dominating sets), A360202 (induced trees). Sequence in context: A049927 A329216 A266616 * A340429 A147679 A339054 Adjacent sequences: A360843 A360844 A360845 * A360847 A360848 A360849 KEYWORD nonn,tabl AUTHOR Andrew Howroyd, Feb 23 2023 STATUS approved

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Last modified September 15 03:00 EDT 2024. Contains 375931 sequences. (Running on oeis4.)