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Search: id:A084486
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| A084486 |
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Number of 4 X n 0-1 matrices which have n+3 1's and have no zero rows or zero columns. |
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+0
2
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| 1, 32, 522, 5776, 50600, 380424, 2570932, 16073600, 94748400, 533515240, 2896652396, 15268777440, 78544641448, 395875164104, 1960998472260, 9570684204544, 46112171619296, 219682468794600, 1036237335593500
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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This is the number of spanning subgraphs of the complete bipartite graph K(4,n) which have n+3 edges. 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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FORMULA
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n/48*((27*4^n-32*3^n+6*2^n)*n^2+(-9*4^n+32*3^n-18*2^n)*n+(-6*4^n+12*2^n)). - Vladeta Jovovic (vladeta(AT)Eunet.yu), May 28 2003
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EXAMPLE
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A84486
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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, el, 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 > for el from 1 to 2^n-1 do > A := Matrix([L[i], L[j], L[k], L[el]]); > if num1s(A, 4, n)=n+3 and (not has(Matrix([1, 1, 1, 1]).A, 0)) then > S := S+1; > end if; > od; > od; > od; > od; > S; > end proc:
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CROSSREFS
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Cf. A001787.
Cf. A084485, A055602, A055603.
Adjacent sequences: A084483 A084484 A084485 this_sequence A084487 A084488 A084489
Sequence in context: A035477 A109384 A125489 this_sequence A010984 A022596 A130609
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KEYWORD
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nonn
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AUTHOR
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W. Edwin Clark (eclark(AT)math.usf.edu), May 27 2003
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), May 28 2003
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