cp's OEIS Frontend

Start with a complete bipartite graph K(6,n) with vertex sets A and B where |A| = 6 and |B| is at least 4. We can arrange the points in sets A and B such that h(A,B) = d(a,b) for all a in A and b in B, where h is the Hausdorff metric. The pair [A,B] is a configuration. Then a set C is between A and B at location s if h(A,C) = h(C,B) = h(A,B) and h(A,C) = s. Call a pair ab, where a is in A and b is in B an edge. This sequence provides the number of sets between sets A' and B' at location s in a new configuration [A',B'] obtained from [A,B] by removing three edges, where exactly two removed edges are incident to the same point in A and exactly two removed edges are incident to the same point in B. So this sequence tells the number of sets at each location on the line segment between A' and B'.

Number of {0,1} 6 X n matrices (with n at least 4) with three fixed zero entries where exactly two zero entries occur in one row and exactly two zero entries occur in one column, with no zero rows or columns.

Take a complete bipartite graph K(6,n) (with n at least 4) having parts A and B where |A| = 6. This sequence gives the number of edge covers of the graph obtained from this K(6,n) graph after removing three edges, where exactly two removed edges are incident to the same vertex in A and exactly two removed edges are incident to the same vertex in B.

Start with a complete bipartite graph K(4,n) with vertex sets A and B where |A| = 4 and |B| is at least 4. We can arrange the points in sets A and B such that h(A,B) = d(a,b) for all a in A and b in B, where h is the Hausdorff metric. The pair [A,B] is a configuration. Then a set C is between A and B at location s if h(A,C) = h(C,B) = h(A,B) and h(A,C) = s. Call a pair ab, where a is in A and b is in B an edge. This sequence provides the number of sets between sets A' and B' at location s in a new configuration [A',B'] obtained from [A,B] by removing three edges, where exactly two of the removed edges are incident to the same point in A but none of the removed edges are incident to the same point in B. So this sequence tells the number of sets at each location on the line segment between A' and B'.

Number of {0,1} 4 X n matrices (with n at least 4) with three fixed zero entries where exactly two zero entries occur in one row and no column has more than one zero entry, with no zero rows or columns.

Take a complete bipartite graph K(4,n) (with n at least 4) having parts A and B where |A| = 4. This sequence gives the number of edge covers of the graph obtained from this K(4,n) graph after removing three edges, where exactly two of the removed edges are incident to the same vertex in A but none of the removed edges are incident to the same vertex in B.

Start with a complete bipartite graph K(3,n) with vertex sets A and B where |A| = 3 and |B| is at least 4. We can arrange the points in sets A and B such that h(A,B) = d(a,b) for all a in A and b in B, where h is the Hausdorff metric. The pair [A,B] is a configuration. Then a set C is between A and B at location s if h(A,C) = h(C,B) = h(A,B) and h(A,C) = s. Call a pair ab, where a is in A and b is in B an edge. This sequence provides the number of sets between sets A' and B' at location s in a new configuration [A',B'] obtained from [A,B] by removing three edges, where exactly two of the removed edges are incident to the same point in A but none of the removed edges are incident to the same point in B. So this sequence tells the number of sets at each location on the line segment between A' and B'.

Number of {0,1} 3 X n matrices (with n at least 4) with three fixed zero entries where exactly two zero entries occur in one row and no column has more than one zero entry, with no zero rows or columns.

Take a complete bipartite graph K(3,n) (with n at least 4) having parts A and B where |A| = 3. This sequence gives the number of edge covers of the graph obtained from this K(3,n) graph after removing three edges, where exactly two of the removed edges are incident to the same vertex in A but none of the removed edges are incident to the same vertex in B.

Start with a complete bipartite graph K(5,n) with vertex sets A and B where |A| = 5 and |B| is at least 4. We can arrange the points in sets A and B such that h(A,B) = d(a,b) for all a in A and b in B, where h is the Hausdorff metric. The pair [A,B] is a configuration. Then a set C is between A and B at location s if h(A,C) = h(C,B) = h(A,B) and h(A,C) = s. Call a pair ab, where a is in A and b is in B an edge. This sequence provides the number of sets between sets A' and B' at location s in a new configuration [A',B'] obtained from [A,B] by removing three edges, where exactly two of the removed edges are incident to the same point in A but none of the removed edges are incident to the same point in B. So this sequence tells the number of sets at each location on the line segment between A' and B'.

Number of {0,1} 5 X n matrices (with n at least 4) with three fixed zero entries where exactly two zero entries occur in one row and no column has more than one zero entry, with no zero rows or columns.

Take a complete bipartite graph K(5,n) (with n at least 4) having parts A and B where |A| = 5. This sequence gives the number of edge covers of the graph obtained from this K(5,n) graph after removing three edges, where exactly two of the removed edges are incident to the same vertex in A but none of the removed edges are incident to the same vertex in B.

Start with a complete bipartite graph K(4,n) with vertex sets A and B where |A| = 4 and |B| is at least 4. We can arrange the points in sets A and B such that h(A,B) = d(a,b) for all a in A and b in B, where h is the Hausdorff metric. The pair [A,B] is a configuration. Then a set C is between A and B at location s if h(A,C) = h(C,B) = h(A,B) and h(A,C) = s. Call a pair ab, where a is in A and b is in B an edge. This sequence provides the number of sets between sets A' and B' at location s in a new configuration [A',B'] obtained from [A,B] by removing three edges, where all three removed edges are incident to different points in A but all three removed edges are incident to the same point in B. So this sequence tells the number of sets at each location on the line segment between A' and B'.

Number of {0,1} 4 X n matrices (with n at least 4) with three fixed zero entries all of which are in the same column with no zero rows or columns.

Take a complete bipartite graph K(4,n) (with n at least 4) having parts A and B where |A| = 4. This sequence gives the number of edge covers of the graph obtained from this K(4,n) graph after removing three edges, where the removed edges are incident to different vertices in A and none of the removed edges are incident to the same vertex in B.

Start with a complete bipartite graph K(6,n) with vertex sets A and B where |A| = 6 and |B| is at least 4. We can arrange the points in sets A and B such that h(A,B) = d(a,b) for all a in A and b in B, where h is the Hausdorff metric. The pair [A,B] is a configuration. Then a set C is between A and B at location s if h(A,C) = h(C,B) = h(A,B) and h(A,C) = s. Call a pair ab, where a is in A and b is in B an edge. This sequence provides the number of sets between sets A' and B' at location s in a new configuration [A',B'] obtained from [A,B] by removing three edges, where all three removed edges are incident to different points in A but all three removed edges are incident to the same point in B. So this sequence tells the number of sets at each location on the line segment between A' and B'.

Number of {0,1} 6 X n matrices (with n at least 4) with three fixed zero entries all of which are in the same column with no zero rows or columns.

Take a complete bipartite graph K(6,n) (with n at least 4) having parts A and B where |A| = 6. This sequence gives the number of edge covers of the graph obtained from this K(6,n) graph after removing three edges, where the removed edges are incident to different vertices in A and none of the removed edges are incident to the same vertex in B.

Start with a complete bipartite graph K(5,n) with vertex sets A and B where |A| = 5 and |B| is at least 4. We can arrange the points in sets A and B such that h(A,B) = d(a,b) for all a in A and b in B, where h is the Hausdorff metric. The pair [A,B] is a configuration. Then a set C is between A and B at location s if h(A,C) = h(C,B) = h(A,B) and h(A,C) = s. Call a pair ab, where a is in A and b is in B an edge. This sequence provides the number of sets between sets A' and B' at location s in a new configuration [A',B'] obtained from [A,B] by removing three edges, where all three removed edges are incident to different points in A but all three removed edges are incident to the same point in B. So this sequence tells the number of sets at each location on the line segment between A' and B'.

Number of {0,1} 5 X n matrices (with n at least 4) with three fixed zero entries all of which are in the same column with no zero rows or columns.

Take a complete bipartite graph K(5,n) (with n at least 4) having parts A and B where |A| = 5. This sequence gives the number of edge covers of the graph obtained from this K(5,n) graph after removing three edges, where the removed edges are incident to different vertices in A and none of the removed edges are incident to the same vertex in B.

Start with a complete bipartite graph K(6,n) with vertex sets A and B where |A| = 6 and |B| is at least 4. We can arrange the points in sets A and B such that h(A,B) = d(a,b) for all a in A and b in B, where h is the Hausdorff metric. The pair [A,B] is a configuration. Then a set C is between A and B at location s if h(A,C) = h(C,B) = h(A,B) and h(A,C) = s. Call a pair ab, where a is in A and b is in B an edge. This sequence provides the number of sets between sets A' and B' at location s in a new configuration [A',B'] obtained from [A,B] by removing three edges, where the removed edges are incident to different points in A and none of the removed edges are incident to the same point in B. So this sequence tells the number of sets at each location on the line segment between A' and B'.

Number of {0,1} 6 X n matrices with three fixed zero entries none of which are in the same row or column with no zero rows or columns.

Take a complete bipartite graph K(6,n) (with n at least 4) having parts A and B where |A| = 6. This sequence gives the number of edge covers of the graph obtained from this K(6,n) graph after removing three edges, where the removed edges are incident to different vertices in A and none of the removed edges are incident to the same vertex in B.

Start with a complete bipartite graph K(5,n) with vertex sets A and B where |A| = 5 and |B| is at least 4. We can arrange the points in sets A and B such that h(A,B) = d(a,b) for all a in A and b in B, where h is the Hausdorff metric. The pair [A,B] is a configuration. Then a set C is between A and B at location s if h(A,C) = h(C,B) = h(A,B) and h(A,C) = s. Call a pair ab, where a is in A and b is in B an edge. This sequence provides the number of sets between sets A' and B' at location s in a new configuration [A',B'] obtained from [A,B] by removing three edges, where the removed edges are incident to different points in A and none of the removed edges are incident to the same point in B. So this sequence tells the number of sets at each location on the line segment between A' and B'.

Number of {0,1} 5 X n matrices with three fixed zero entries none of which are in the same row or column with no zero rows or columns.

Take a complete bipartite graph K(5,n) (with n at least 4) having parts A and B where |A| = 5. This sequence gives the number of edge covers of the graph obtained from this K(5,n) graph after removing three edges, where the removed edges are incident to different vertices in A and none of the removed edges are incident to the same vertex in B.

Start with a complete bipartite graph K(4,n) with vertex sets A and B where |A| = 4 and |B| is at least 4. We can arrange the points in sets A and B such that h(A,B) = d(a,b) for all a in A and b in B, where h is the Hausdorff metric. The pair [A,B] is a configuration. Then a set C is between A and B at location s if h(A,C) = h(C,B) = h(A,B) and h(A,C) = s. Call a pair ab, where a is in A and b is in B an edge. This sequence provides the number of sets between sets A' and B' at location s in a new configuration [A',B'] obtained from [A,B] by removing three edges, where the removed edges are incident to different points in A and none of the removed edges are incident to the same point in B. So this sequence tells the number of sets at each location on the line segment between A' and B'.

Number of {0,1} 4 X n matrices (with n at least 4) with three fixed zero entries none of which are in the same row or column with no zero rows or columns.

Take a complete bipartite graph K(4,n) (with n at least 4) having parts A and B where |A| = 4. This sequence gives the number of edge covers of the graph obtained from this K(4,n) graph after removing three edges, where the removed edges are incident to different vertices in A and none of the removed edges are incident to the same vertex in B.