login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A327728 Number of unlabeled multigraphs with loops allowed and n edges covering three vertices. 2
0, 2, 8, 19, 40, 77, 132, 217, 340, 510, 742, 1054, 1456, 1976, 2634, 3453, 4464, 5703, 7194, 8987, 11120, 13636, 16588, 20036, 24024, 28630, 33916, 39951, 46816, 54601, 63376, 73253, 84324, 96690, 110466, 125778, 142728, 161468, 182126, 204841, 229768, 257075, 286902, 319447, 354880, 393384 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (2,1,-2,-3,0,6,0,-3,-2,1,2,-1).

FORMULA

a(n) = A050531(n) - A002620(n+2).

a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - 3*a(n-4) + 6*a(n-6) - 3*a(n-8) - 2*a(n-9) + a(n-10) + 2*a(n-11) - a(n-12) for n > 12.

G.f.: x^2*(2 + 4*x + x^2 - 2*x^3 + x^6)/((1 - x)^6*(1 + x)^2*(1 + x + x^2)^2).

EXAMPLE

a(2) = 2 since three vertices may be covered with two edges in 2 ways: the path graph P(3) or an edge plus a loop.

PROG

(PARI) concat([0], Vec((2 + 4*x + x^2 - 2*x^3 + x^6)/((1 - x)^6*(1 + x)^2*(1 + x + x^2)^2) + O(x^40)))

CROSSREFS

Column k=3 of A327615.

Cf. A002620, A050531.

Sequence in context: A193389 A030504 A240279 * A000158 A101427 A286269

Adjacent sequences:  A327725 A327726 A327727 * A327729 A327730 A327731

KEYWORD

nonn,easy

AUTHOR

Andrew Howroyd, Oct 23 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 27 12:49 EDT 2022. Contains 357057 sequences. (Running on oeis4.)