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A059441 Triangle T(n,k) (n >= 1, 0 <= k <= n-1) giving number of regular labeled graphs with n nodes and degree k, read by rows. 23
1, 1, 1, 1, 0, 1, 1, 3, 3, 1, 1, 0, 12, 0, 1, 1, 15, 70, 70, 15, 1, 1, 0, 465, 0, 465, 0, 1, 1, 105, 3507, 19355, 19355, 3507, 105, 1, 1, 0, 30016, 0, 1024380, 0, 30016, 0, 1, 1, 945, 286884, 11180820, 66462606, 66462606, 11180820, 286884, 945, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,8
REFERENCES
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 279.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..300 (rows 1..24)
Denis S. Krotov, [[2,10],[6,6]]-equitable partitions of the 12-cube, arXiv:2012.00038 [math.CO], 2020.
Brendan D. McKay, Applications of a technique for labeled enumeration, Congress. Numerantium, 40 (1983), 207-221. See page 216.
Wikipedia, Regular graph
EXAMPLE
1;
1, 1;
1, 0, 1;
1, 3, 3, 1;
1, 0, 12, 0, 1;
1, 15, 70, 70, 15, 1;
1, 0, 465, 0, 465, 0, 1;
1, 105, 3507, 19355, 19355, 3507, 105, 1;
1, 0, 30016, 0, 1024380, ...;
1, 945, 286884, 11180820, 66462606, ...;
1, 0, 3026655, 0, 5188453830, ...;
MATHEMATICA
Table[SeriesCoefficient[Product[1+Times@@x/@s, {s, Subsets[Range[n], {2}]}], Sequence@@Table[{x[i], 0, k}, {i, n}]], {n, 9}, {k, 0, n-1}] (* Gus Wiseman, Dec 24 2018 *)
PROG
(PARI) for(n=1, 10, print(A059441(n))) \\ See A295193 for script, Andrew Howroyd, Aug 28 2019
CROSSREFS
Row sums are A295193.
Columns: A123023 (k=1), A001205 (k=2), A002829 (k=3, with alternating zeros), A005815 (k=4), A338978 (k=5, with alternating zeros), A339847 (k=6).
Cf. A051031 (unlabeled case), A324163 (connected case), A333351 (multigraphs).
Sequence in context: A283798 A065551 A283797 * A186028 A225054 A355604
KEYWORD
tabl,nice,nonn
AUTHOR
N. J. A. Sloane, Feb 01 2001
EXTENSIONS
a(37)-a(55) from Andrew Howroyd, Aug 25 2017
STATUS
approved

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Last modified March 29 09:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)