This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A324221 #23 Jun 02 2025 17:24:13
%S A324221 0,1,6,15,36,72,139,244,414,663,1030,1540,2247,3187,4433,6036,8088,
%T A324221 10658,13861,17785,22571,28329,35227,43401,53049,64333,77485,92697,
%U A324221 110235,130324,153268,179326,208843,242115,279529,321422,368226,420319,478182,542238,613017
%N A324221 Number of connected 2n-regular loopless multigraphs with five nodes.
%C A324221 There are no (2n+1)-regular multigraphs satisfying the condition above.
%C A324221 Multigraphs are loopless.
%C A324221 Initial terms computed with 'Nauty and Traces'.
%H A324221 Brendan McKay and Adolfo Piperno, <a href="http://pallini.di.uniroma1.it">Nauty and Traces</a>
%F A324221 Conjectures from _Colin Barker_, Feb 18 2019: (Start)
%F A324221 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)).
%F A324221 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.
%F A324221 (End)
%F A324221 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
%o A324221 (nauty) for ((n=0;n<76;n=n+2)); do geng -c -d1 5 -q | multig -m${n} -u; done
%Y A324221 Row n=5 of A328682.
%K A324221 nonn
%O A324221 0,3
%A A324221 _Natan Arie Consigli_, Feb 18 2019
%E A324221 a(28)-a(30) from _Andrew Howroyd_, Mar 18 2020