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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
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
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 March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)