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 A303208 Number of total dominating sets in the n X n rook graph. 2
 0, 9, 334, 53731, 30844786, 66544564805, 556588617042914, 18376877842518517955, 2414913046805958120844234, 1267171440764716263069641387581, 2658150749788131925244338204731596650, 22299981643440069703358952237798936248817875 (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, Rook Graph Eric Weisstein's World of Mathematics, Total Dominating Set FORMULA a(n) = Sum_{k=0..n} (-1)^k*binomial(n,k)^2*k!*A287065(n-k). - Andrew Howroyd, Apr 20 2018 a(n) ~ 2^(n^2). - Vaclav Kotesovec, Apr 20 2018 MATHEMATICA b[0] = 1; b[n_] := (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}]; Table[Sum[(-1)^k Binomial[n, k]^2 k! b[n - k], {k, 0, n}], {n, 10}] PROG (PARI) \\ here c(n) is A287065. b(m, n)=sum(j=0, m, (-1)^j*binomial(m, j)*(2^(m - j) - 1)^n); c(n)=(2^n-1)^n + sum(i=1, n-1, b(n, i)*binomial(n, i)); a(n) = {sum(k=0, n, (-1)^k*binomial(n, k)^2*k!*c(n-k))} \\ Andrew Howroyd, Apr 20 2018 CROSSREFS Cf. A287065, A289196, A303211. Sequence in context: A289196 A266907 A288547 * A196883 A012105 A100569 Adjacent sequences: A303205 A303206 A303207 * A303209 A303210 A303211 KEYWORD nonn AUTHOR Eric W. Weisstein, Apr 19 2018 EXTENSIONS Terms a(6) and beyond from Andrew Howroyd, Apr 20 2018 STATUS approved

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Last modified June 4 01:00 EDT 2023. Contains 363118 sequences. (Running on oeis4.)