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 A286189 Number of connected induced (non-null) subgraphs of the n X n rook graph. 18
 1, 13, 397, 55933, 31450861, 67253507293, 559182556492477, 18408476382988290493, 2416307646576708948065581, 1267404418454077249779938768413, 2658301080374793666228695738368407037, 22300360304310794054520197736231374212892413 (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, Vertex-Induced Subgraph FORMULA a(n) = Sum_{i=1..n} Sum_{j=1..n} binomial(n,i)*binomial(n,j)*A262307(i,j). - Andrew Howroyd, May 22 2017 a(n) ~ 2^(n^2). - Vaclav Kotesovec, Oct 12 2017 MATHEMATICA {1} ~ Join ~ Table[g = GraphData[{"Rook", {n, n}}]; -1 + ParallelSum[ Boole@ ConnectedGraphQ@ Subgraph[g, s], {s, Subsets@ Range[n^2]}], {n, 2, 4}] (* Second program: *) (* b = A183109, T = A262307 *) b[n_, m_] := Sum[(-1)^j*Binomial[m, j]*(2^(m - j) - 1)^n, {j, 0, m}]; T[m_, n_] := T[m, n] = b[m, n] - Sum[T[i, j]*b[m - i, n - j] Binomial[m - 1, i - 1]*Binomial[n, j], {i, 1, m - 1}, {j, 1, n - 1}]; a[n_] := Sum[Binomial[n, i]*Binomial[n, j]*T[i, j], {i, 1, n}, {j, 1, n}]; Array[a, 12] (* Jean-François Alcover, Oct 11 2017, after Andrew Howroyd *) PROG (PARI) G(N)={my(S=matrix(N, N), T=matrix(N, N), U=matrix(N, N)); \\ S is A183109, T is A262307, U is mxn variant of this sequence. for(m=1, N, for(n=1, N, S[m, n]=sum(j=0, m, (-1)^j*binomial(m, j)*(2^(m - j) - 1)^n); T[m, n]=S[m, n]-sum(i=1, m-1, sum(j=1, n-1, T[i, j]*S[m-i, n-j]*binomial(m-1, i-1)*binomial(n, j))); U[m, n]=sum(i=1, m, sum(j=1, n, binomial(m, i)*binomial(n, j)*T[i, j])) )); U} a(n)=G(n)[n, n]; \\ Andrew Howroyd, May 22 2017 CROSSREFS Cf. A262307, A183109. Cf. A020873 (wheel), A059020 (ladder), A059525 (grid), A286139 (king), A286182 (prism), A286183 (antiprism), A286184 (helm), A286185 (Möbius ladder), A286186 (friendship), A286187 (web), A286188 (gear), A285765 (queen). Sequence in context: A013527 A009010 A171196 * A280553 A162446 A284824 Adjacent sequences:  A286186 A286187 A286188 * A286190 A286191 A286192 KEYWORD nonn AUTHOR Giovanni Resta, May 04 2017 EXTENSIONS Terms a(7) and beyond from Andrew Howroyd, May 22 2017 STATUS approved

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Last modified May 28 03:28 EDT 2022. Contains 354110 sequences. (Running on oeis4.)