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A324221 Number of connected 2n-regular loopless multigraphs with five nodes. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 11 01:19 EDT 2020. Contains 335600 sequences. (Running on oeis4.)