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 A084485 Number of 3 X n 0-1 matrices which have n+2 1's and have no zero rows or zero columns. 1
 1, 12, 90, 522, 2595, 11673, 49014, 195828, 753813, 2819475, 10308144, 36998118, 130786695, 456452493, 1575799290, 5389290792, 18281487081, 61569776727, 206040460212, 685584843450, 2269566343611, 7478425876977, 24538396875870, 80206515476892, 261239771497725 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This is the number of spanning subgraphs of the complete bipartite graph K(3,n) with n + 2 edges and no isolated vertices. If the subgraphs are also connected then they are spanning trees. The number of spanning trees in K(m,n) is known. See A001787. REFERENCES M. Janjic and B. Petkovic, A Counting Function, arXiv preprint arXiv:1301.4550, 2013. - From N. J. A. Sloane, Feb 13 2013 LINKS FORMULA a(n) = n*(4*(3*n-1)*3^n-9*(n-1)*2^n)/24. - Vladeta Jovovic, May 28 2003 G.f.: x*(1-3*x+3*x^2-17*x^3+33*x^4)/((3*x-1)^3*(2*x-1)^3). - Alois P. Heinz, Sep 24 2012 MAPLE with(LinearAlgebra): num1s:= (M, m, n)->add(ListTools[Flatten](convert(M, listlist))[j], j=1..m*n): binrows:= n->[seq(convert(i+2^n, base, 2)[1..n], i=1..2^n-1)]: a:= proc(n) local A, L, i, j, k, S, M: S := 0: L := binrows(n): for i from 1 to 2^n-1 do for j from 1 to 2^n-1 do for k from 1 to 2^n-1 do A := Matrix([L[i], L[j], L[k]]); if num1s(A, 3, n)=n+2 and (not has(Matrix([1, 1, 1]).A, 0)) then S := S+1; end if; od; od; od; S; end proc: seq (a(n), n=1..5); CROSSREFS Cf. A001787. Cf. A084486, A055602, A055603. Sequence in context: A121590 A186209 A005758 * A130072 A135158 A073382 Adjacent sequences:  A084482 A084483 A084484 * A084486 A084487 A084488 KEYWORD nonn AUTHOR W. Edwin Clark, May 27 2003 EXTENSIONS More terms from Vladeta Jovovic, May 28 2003 Comment corrected by W. Edwin Clark, Sep 24 2012 STATUS approved

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