|
Search: id:A084485
|
|
|
| A084485 |
|
Number of 3 X n 0-1 matrices which have n+2 1's and have no zero rows or zero columns. |
|
+0
2
|
|
| 1, 12, 90, 522, 2595, 11673, 49014, 195828, 753813, 2819475, 10308144, 36998118, 130786695, 456452493, 1575799290, 5389290792, 18281487081, 61569776727, 206040460212, 685584843450, 2269566343611, 7478425876977, 24538396875870
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
This is the number of spanning subgraphs of the complete bipartite graph K(3,n). If the subgraphs are also connected then they are spanning trees. The number of spanning trees in K(m,n) is known. See A001787.
|
|
FORMULA
|
n*(4*(3*n-1)*3^n-9*(n-1)*2^n)/24. - Vladeta Jovovic (vladeta(AT)Eunet.yu), May 28 2003
|
|
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:
|
|
CROSSREFS
|
Cf. A001787.
Cf. A084486, A055602, A055603.
Adjacent sequences: A084482 A084483 A084484 this_sequence A084486 A084487 A084488
Sequence in context: A034197 A121590 A005758 this_sequence A135158 A130072 A073382
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
W. Edwin Clark (eclark(AT)math.usf.edu), May 27 2003
|
|
EXTENSIONS
|
More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), May 28 2003
|
|
|
Search completed in 0.002 seconds
|
