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Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!) A369692 Connected domination number of the n X n grid graph. 2 1, 2, 3, 7, 11, 14, 20, 26, 30, 39, 47, 52, 64, 74, 80, 95 (list; graph; refs; listen; history; text; internal format) OFFSET 1,2 LINKS Table of n, a(n) for n=1..16. Alexander D. Healy, Examples of (near-)optimal dominating sets for n <= 12 Eric Weisstein's World of Mathematics, Connected Domination Number. Eric Weisstein's World of Mathematics, Grid Graph. FORMULA a(3*n) <= n*(3*n+1); a(3*n-1) <= 3*n^2 - 1; a(3*n-2) <= (n-1)*(3*n+1). Conjecturally these inequalities hold with equality for n > 1. - Andrew Howroyd, Mar 06 2024 EXAMPLE From Andrew Howroyd, Mar 06 2024: (Start) a(16) = 95 = 16 + 5*14 + 4*2 + 1. . . . . . . . . . . . . . . . . X X X X X X X X X X X X X X X X . X . . X . . X . . X . . X . . . X . . X . . X . . X . . X . . . X . . X . . X . . X . . X X X . X . . X . . X . . X . . X . . . X . . X . . X . . X . . X . . . X . . X . . X . . X . . X X X . X . . X . . X . . X . . X . . . X . . X . . X . . X . . X . . . X . . X . . X . . X . . X X X . X . . X . . X . . X . . X . . . X . . X . . X . . X . . X . . . X . . X . . X . . X . . X X X . X . . X . . X . . X . . X . . . X . . X . . X . . X . . X X . (End) CROSSREFS Cf. A104519, A287690, A302488, A370428. Sequence in context: A040152 A323353 A188529 * A174060 A285278 A092353 Adjacent sequences: A369689 A369690 A369691 * A369693 A369694 A369695 KEYWORD nonn,more AUTHOR Alexander D. Healy, Feb 25 2024 EXTENSIONS a(10)-a(16) from Andrew Howroyd, Feb 25 2024 STATUS approved

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Last modified August 30 07:09 EDT 2024. Contains 375532 sequences. (Running on oeis4.)