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A331504 Number of labeled graphs with n nodes and floor(n*(n-1)/4) edges. 1
1, 1, 3, 20, 252, 6435, 352716, 40116600, 9075135300, 4116715363800, 3824345300380220, 7219428434016265740, 27217014869199032015600, 205397724721029574666088520, 3136262529306125724764953838760 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
The expected number of edges of a random graph is n*(n - 1)/4. [See the Cieslik reference.]
REFERENCES
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 109.
LINKS
Dietmar Cieslik, Counting Networks.
FORMULA
a(n) = binomial(binomial(n,2), floor(n*(n-1)/4)).
EXAMPLE
a(4) is 20 because for n=4, floor(n*(n-1)/4) = 3, and there are A000717(4) = 3 graphs with four points and three edges. See figure below or J. Riordan reference.
The non-isomorphic graphs with four nodes and three edges along with the corresponding number of labeled graphs are as follows:
.
*--* *--* *
| / | |
|/ * | |
* *--* *--*--*
4 12 4
PROG
(PARI) a(n) = binomial(binomial(n, 2), n*(n-1)\4);
CROSSREFS
Cf. A000717 ("unlabeled case"), A084546.
Sequence in context: A262208 A324955 A183607 * A197322 A197975 A210906
KEYWORD
nonn
AUTHOR
Washington Bomfim, Jan 18 2020
STATUS
approved

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Last modified March 19 01:34 EDT 2024. Contains 370952 sequences. (Running on oeis4.)