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 A287065 Number of dominating sets on the n X n rook graph. 4
 1, 11, 421, 59747, 32260381, 67680006971, 559876911043381, 18412604442711949187, 2416403019417984915336061, 1267413006543912045144741284411, 2658304092145691708492995820522716981, 22300364428188338185156192161829091442585827 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..50 Eric Weisstein's World of Mathematics, Dominating Set Eric Weisstein's World of Mathematics, Rook Graph FORMULA a(n) = (2^n-1)^n + Sum_{i=1..n-1} binomial(n,i) * A183109(n,i). - Andrew Howroyd, May 22 2017 MATHEMATICA Table[(2^n - 1)^n + Sum[Binomial[n, i] Sum[(-1)^j (-1 + 2^(n - j))^i Binomial[n, j], {j, 0, n}], {i, n - 1}], {n, 20}] (* Eric W. Weisstein, May 27 2017 *) PROG (PARI) b(m, n)=sum(j=0, m, (-1)^j*binomial(m, j)*(2^(m - j) - 1)^n); a(n)=(2^n-1)^n + sum(i=1, n-1, b(n, i)*binomial(n, i)); \\ Andrew Howroyd, May 22 2017 CROSSREFS Main diagonal of A287274. Cf. A183109, A002720. Sequence in context: A090558 A068135 A197770 * A337527 A356210 A140840 Adjacent sequences: A287062 A287063 A287064 * A287066 A287067 A287068 KEYWORD nonn AUTHOR Eric W. Weisstein, May 19 2017 EXTENSIONS a(6)-a(12) from Andrew Howroyd, May 22 2017 STATUS approved

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Last modified September 30 07:44 EDT 2023. Contains 365781 sequences. (Running on oeis4.)