A186417 The number of unlabeled graphs on n nodes with degree of 1 or 2.

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

Offset: 0

Author

Geoffrey Critzer, Feb 21 2011

Keywords

• nonn

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

• Andrew Howroyd, Table of n, a(n) for n = 0..1000

Programs

Mathematica

CoefficientList[Series[1/(1-x^2) Product[1/(1-x^i)^2,{i,3,20}],{x,0,20}],x]

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

Formula

O.g.f.: (1/(1-x^2)) * Product_{i>=3} 1/(1-x^i)^2.

Extensions

Terms a(21) and beyond from Andrew Howroyd, Oct 20 2018