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A084485
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Number of 3 X n 0-1 matrices which have n+2 1's and have no zero rows or zero columns.
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1
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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
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OFFSET
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1,2
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COMMENTS
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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.
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REFERENCES
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M. Janjic and B. Petkovic, A Counting Function, arXiv preprint arXiv:1301.4550, 2013. - From N. J. A. Sloane, Feb 13 2013
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LINKS
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Table of n, a(n) for n=1..25.
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FORMULA
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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
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MAPLE
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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);
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CROSSREFS
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Cf. A001787.
Cf. A084486, A055602, A055603.
Sequence in context: A121590 A186209 A005758 * A130072 A135158 A073382
Adjacent sequences: A084482 A084483 A084484 * A084486 A084487 A084488
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KEYWORD
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nonn
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AUTHOR
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W. Edwin Clark, May 27 2003
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EXTENSIONS
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More terms from Vladeta Jovovic, May 28 2003
Comment corrected by W. Edwin Clark, Sep 24 2012
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STATUS
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approved
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