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# User:Marko Riedel

From OeisWiki

B.Sc. Computer Science from UBC 1994, M.Sc. Computer Science from University of Toronto 1996.

Some sequences that I contributed / modified:

- A230367 Number of graphs on n vertices with edges colored with at most three interchangeable colors under the symmetries of the full edge permutation group
- A233748 Number of graphs on n vertices with edges colored with at most four interchangeable colors under the symmetries of the full edge permutation group
- A233894 Number of graphs on n vertices with edges colored with at most five interchangeable colors under the symmetries of the full edge permutation group
- A309116 Colorings of the complete graph Kn with any number of swappable colors
- A306393, Average number of inversions in a full binary heap
- A368213, Number of permutations of n elements that factor into exactly k-cycles
- A053515, Number of connected directed 3-multigraphs on n nodes
- A053466, Number of connected 3-multigraphs on n nodes
- A362657, Number of bracelets consisting of three instances each of n swappable colors
- A362658, Number of bracelets consisting of four instances each of n swappable colors
- A362659, Number of bracelets consisting of five instances each of n swappable colors
- A054499, Number of bracelets consisting of two instances each of n swappable colors / Number of pairings on a bracelet
- A360037, Multiset partitions into subsets of (1,1,1,2,2,2,..,n,n,n)
- A360038, Multiset partitions into subsets of (1,1,1,1,2,2,2,2,..,n,n,n,n)
- A360039, Multiset partitions into subsets of (1,1,1,1,1,2,2,2,2,2,..,n,n,n,n,n)
- A358710, Multiset partitions into submultisets of (1,1,2,2,..,n,n)
- A358721, Multiset partitions into submultisets of (1,1,1,2,2,2,..,n,n,n)
- A358722, Multiset partitions into submultisets of (1,1,1,1,2,2,2,2,..,n,n,n,n)
- A358781, Total multiset partitions of (1,1,1,1,2,2,2,2,..,n,n,n,n)
- A357536, Number of colorings of an n X n grid with at most n interchangeable colors under rotational and reflectional symmetry
- A264741, Number of colorings of an n X n grid with at most three interchangeable colors under rotational and reflectional symmetry
- A264742, Number of colorings of an n X n grid with at most four interchangeable colors under rotational and reflectional symmetry
- A355502, Number of inequivalent simultaneous colorings of the faces, vertices and edges of the cube under rotational symmetry using exactly n colors
- A356685, Number of inequivalent simultaneous colorings of the faces, vertices and edges of the cube under rotational symmetry using at most n colors
- A003692, Number of trees on n labeled vertices with degree at most 3
- A058001, Number of 3 X 3 matrices with entries mod n, up to row and column permutation
- A355023, Number of labeled trees on n nodes with maximum degree three and three vertices of degree three
- A355024, Number of unlabeled trees on n nodes with maximum degree three and three vertices of degree three
- A250308, Unrooted unlabeled odd degree trees with 2n nodes
- A060279, Rooted labeled odd degree trees with 2n nodes
- A007106, Labeled odd degree trees with 2n nodes
- A093352, Number of labeled n-vertex graphs without a 2-component
- A200091, The number of ways of putting n labeled items into k labeled boxes so that each box receives at least 2 objects
- A351356, Binary necklaces with at least two consecutive black beads, classified by number of black beads
- A351357, Binary necklaces with at least three consecutive black beads, classified by number of black beads
- A351358, Binary necklaces with at least four consecutive black beads, classified by number of black beads
- A351359, Binary necklaces with at least two consecutive black beads
- A351360, Binary necklaces with at least three consecutive black beads
- A351361, Binary necklaces with at least four consecutive black beads
- A351363, Binary necklaces with at least four consecutive black beads and n black and n white beads
- A351364, Binary necklaces with at most three consecutive black beads and n black and n white beads
- A076263, Connected unlabeled graphs
- A283753, Weakly connected unlabeled digraphs
- A000666, Enumerating graphs with self-loops
- A000088, Enumerating ordinary graphs
- A088957, Labeled forests in the complete graph
- A000246, Permutations of odd order
- A007018, Non-isomorphic two-colorings of full binary trees
- A152176, Coloring bracelets with swappable colors, generating function
- A071720, Spanning trees of Kn minus an edge
- A002626, Generating function of inequivalent colorings of a 2xN board with C colors under row and column permutations
- A001678, Generating functions of unordered rooted trees with n nodes where nodes cannot have out-degree 1, classified by the number of leaves, using the Polya Enumeration Theorem and the exponential formula
- A000169, The tree function and Eulerian numbers of the second order
- A208539, Proper colorings of necklaces / bracelets
- A331951, Number of binary trees with n internal nodes that contain the subtree (Z, (Z, U, U), (Z, U, U))
- A332496, Triangular array T(n,k): the number of non-isomorphic colorings of K_n minus an edge using exactly k colors
- A331538, Number of functions f:1..n -> 1..n such that there exists a k such that |f^(-1)(k)| = k
- A331106, Number of plane trees of total weight n of combinatorial class T=Z*U + Z*T^2/(1-T) with nodes Z of weight one and leaves U of weight three
- A331013, Number of unlabeled bicolored bipartite graphs on 2n nodes having n nodes of each color with no edges between vertices of the same color and edges having two colors and allowing the node color classes to be interchanged. Edge colors are swappable (permuted by the symmetric group)
- A001263, Narayana numbers count unlabeled ordered rooted trees on n nodes having k leaves, proof
- A323875, Number of labeled graphs on n nodes with two connected components
- A323876, Number of labeled graphs on n nodes with three connected components
- A323877, Number of labeled graphs on n nodes with four connected components
- A143543, Triangle read by rows: T(n,k) = number of labeled graphs on n nodes with k connected components, 1<=k<=n.
- A056292, Necklace colorings with four swappable colors
- A002076, Necklace colorings with three swappable colors
- A306194, Non-isomorphic colorings of the edges of a cube using at most n colors under rotational symmetries and permutations of the colors
- A000009, Number of partitions into distinct parts
- A001429, Number of n-node connected unicyclic unlabelled graphs
- A321244, Non-isomorphic proper colorings of the 3 X 3 grid graph using at most n colors under rotational and reflectional symmetries
- A304482, Number A(n,k) of n-element subsets of 1..kn whose elements sum to a multiple of n
- A316093, Non-isomorphic colorings of the cube under rotations, using at most N colors on the faces and M colors on the vertices
- A244581, Multisets of multisets corresponding to integer partitions lambda, drawn from |lambda| symbols, where the sizes of the multisets are given by the elements of lambda as is the total number of occurrences of each symbol
- A294198, Labeled trees with at least one node of degree two
- A299104, A class of boolean functions under permutation / complementation of inputs, complementation of outputs
- A294198, Labeled trees with at least one node of degree two
- A298637, Generalized Catalan numbers (well-formed parentheses in words)
- A296143, Rows of beads under reflections and color swaps
- A294791, Colordings of the torus under rotational symmetry and swappable colors
- A292553, Number of rooted unlabeled trees on n nodes where each node has at most 8 children
- A007139, Number of unlabeled bicolored bipartite graphs on 2n nodes having n nodes of each color with no edges between vertices of the same color and allowing the color classes to be interchanged
- A284664, Number of proper colorings of the 2n-gon with 2 instances of each of n colors under rotational symmetry
- A283755, Number of non-isomorphic unlabeled connected graphs with loops on n nodes and with k edges
- A283153, Number of set partitions of unique elements from an n X 4 matrix where elements from the same row may not be in the same partition
- A281582, Number of rolls of a die with n sides that maximizes the average ratio of highest number of occurrences of a face value to lowest number
- A279514 Number of terms in the cycle index Z(S_n X S_n) of the Cartesian product of the symmetric group S_n with itself that contain q cycles, where 1 <= q <= n*n
- A277840 Number of finite automata with n states, n input symbols and two output symbols
- A277073 Number of n-node labeled graphs with two endpoints
- A274056 Number of unrooted labeled trees on 2n nodes with node degree either one or three