%I #11 Mar 06 2021 13:03:36
%S 0,1,3,7,13,25,40,65,99,146,208,294,399,538,711,926,1188,1513,1896,
%T 2361,2910,3557,4312,5199,6214,7392,8739,10276,12019,14002,16224,
%U 18732,21537,24669,28152,32031,36309,41047,46263,51997,58282,65176,72688,80894,89820,99518
%N Number of unlabeled loopless multigraphs with n edges covering four vertices.
%H Andrew Howroyd, <a href="/A328652/b328652.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,0,-2,-2,3,0,3,-2,-2,0,0,2,-1).
%F a(n) = A003082(n) - A001399(n).
%F a(n) = 2*a(n-1) - 2*a(n-4) - 2*a(n-5) + 3*a(n-6) + 3*a(n-8) - 2*a(n-9) - 2*a(n-10) + 2*a(n-13) - a(n-14) for n > 14.
%F G.f.: x^2*(1 + x + x^2 - x^3 + x^4 - 2*x^5 + 2*x^6)/((1 - x)^6*(1 + x)^2*(1 + x^2)*(1 + x + x^2)^2).
%t LinearRecurrence[{2,0,0,-2,-2,3,0,3,-2,-2,0,0,2,-1},{0,1,3,7,13,25,40,65,99,146,208,294,399,538},50] (* _Harvey P. Dale_, Mar 06 2021 *)
%o (PARI) concat([0], Vec((1 + x + x^2 - x^3 + x^4 - 2*x^5 + 2*x^6)/((1 - x)^6*(1 + x)^2*(1 + x^2)*(1 + x + x^2)^2) + O(x^40)))
%Y Column k=4 of A309936.
%Y Cf. A001399, A003082.
%K nonn,easy
%O 1,3
%A _Andrew Howroyd_, Oct 23 2019