A324221 Number of connected 2n-regular loopless multigraphs with five nodes.

0, 1, 6, 15, 36, 72, 139, 244, 414, 663, 1030, 1540, 2247, 3187, 4433, 6036, 8088, 10658, 13861, 17785, 22571, 28329, 35227, 43401, 53049, 64333, 77485, 92697, 110235, 130324, 153268, 179326, 208843, 242115, 279529, 321422, 368226, 420319, 478182, 542238, 613017

Offset

0,3

Comments

There are no (2n+1)-regular multigraphs satisfying the condition above.

Multigraphs are loopless.

Initial terms computed with 'Nauty and Traces'.

Links

Table of n, a(n) for n=0..40.

Brendan McKay and Adolfo Piperno, Nauty and Traces

Formula

Conjectures from Colin Barker, Feb 18 2019: (Start)

G.f.: x*(1 + 3*x - x^2 + 4*x^3 - x^4 + 6*x^5 + 4*x^7 - x^8 - x^9 + x^10) / ((1 - x)^6*(1 + x)^2*(1 + x^2)*(1 + x + x^2)).

a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4) - 2*a(n-5) + 4*a(n-6) - 2*a(n-7) + a(n-8) - a(n-9) - 2*a(n-10) + 3*a(n-11) - a(n-12) for n>11.

(End)

Equivalent conjecture: 1152*a(n) = 6*n^5 + 30*n^4 + 220*n^3 + 540*n^2 + 1143*n - 353 + 72*A056594(n) + 128*A049347(n) + 153*A181983(n+1). - R. J. Mathar, Mar 09 2019

Prog

(nauty/shell) for ((n=0; n<76; n=n+2)); do geng -c -d1 5 -q | multig -m${n} -u; done

Crossrefs

Row n=5 of A328682.

Sequence in context: A074149 A273411 A273490 * A177206 A128443 A245470

Adjacent sequences: A324218 A324219 A324220 * A324222 A324223 A324224

Keyword

nonn

Author

Natan Arie Consigli, Feb 18 2019

Extensions

a(28)-a(30) from Andrew Howroyd, Mar 18 2020

Status

approved