|
|
A186417
|
|
The number of unlabeled graphs on n nodes with degree of 1 or 2
|
|
3
|
|
|
1, 0, 1, 2, 3, 4, 8, 10, 17, 24, 36, 50, 76, 102, 148, 204, 285, 386, 537, 718, 980, 1308, 1756, 2324, 3097, 4060, 5353, 6986, 9124, 11822, 15341, 19748, 25442, 32586, 41705, 53124, 67628, 85692, 108501, 136870, 172430, 216528, 271578, 339578, 424073
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
COMMENTS
|
The partial sums give the number of unlabeled graphs on n nodes of degree 0, 1, or 2.
|
|
REFERENCES
|
Herbert S. Wilf, Generatingfunctiontology, Academic Press, p. 106.
|
|
LINKS
|
|
|
FORMULA
|
O.g.f.: (1/(1-x^2)) * Product_{i>=3} 1/(1-x^i)^2.
|
|
MATHEMATICA
|
CoefficientList[Series[1/(1-x^2) Product[1/(1-x^i)^2, {i, 3, 20}], {x, 0, 20}], x]
|
|
PROG
|
(PARI) seq(n)={Vec(prod(i=3, n, 1/(1-x^i)^2 + O(x*x^n))/(1-x^2))} \\ Andrew Howroyd, Oct 20 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|