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

Author

Natan Arie Consigli, Feb 18 2019

Keywords

• nonn

Comments

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

Multigraphs are loopless.

Initial terms computed with 'Nauty and Traces'.

Links

• Brendan McKay and Adolfo Piperno, Nauty and Traces

Crossrefs

Row n=5 of A328682.

Programs

nauty

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

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

Extensions

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