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A240168
T(n,k) is the number of unlabeled graphs of n vertices and k edges that have endpoints, where an endpoint is a vertex with degree 1.
1
0, 1, 1, 1, 1, 2, 2, 1, 1, 2, 3, 5, 4, 2, 1, 1, 2, 4, 8, 13, 15, 16, 11, 5, 2, 1, 1, 2, 4, 9, 19, 35, 55, 75, 83, 72, 51, 29, 13, 5, 2, 1, 1, 2, 4, 10, 22, 50, 105, 196, 338, 511, 649, 695, 627, 473, 304, 172, 83, 35, 14, 5, 2, 1
OFFSET
1,6
COMMENTS
The length of the rows are 1,1,2,4,7,11,16,22,...: (n-1)*(n-2)/2 + 1 = A152947(n).
T(n,k) = 0 if k > (n-1)*(n-2)/2 + 1. (Cf. A245796)
EXAMPLE
First few rows of irregular triangle are:
..0
..1
..1....1
..1....2....2....1
..1....2....3....5....4....2....1
..1....2....4....8...13...15...16...11....5....2....1
..1....2....4....9...19...35...55...75...83...72...51...29...13....5....2....1
...
CROSSREFS
Cf. A245796. Sum of n-th row is equal to A141580(n).
Sequence in context: A220603 A238404 A331910 * A199204 A262750 A075402
KEYWORD
nonn,tabf
AUTHOR
Chai Wah Wu, Aug 02 2014
STATUS
approved