cp's OEIS Frontend

A345132 Number of (n+2) X (n+2) symmetric matrices with nonnegative integer entries, trace 0, with n rows that sum to 2, and 2 rows that sum to 1.

%I A345132 #48 Jul 01 2021 23:56:11
%S A345132 1,1,3,10,46,252,1642,12316,104730,995122,10450414,120192924,
%T A345132 1502537932,20285580880,294156077364,4559608340968,75236088623548,
%U A345132 1316668510772124,24358939966126900,475008770990906488,9737844963832507656,209366721066736679536
%N A345132 Number of (n+2) X (n+2) symmetric matrices with nonnegative integer entries, trace 0, with n rows that sum to 2, and 2 rows that sum to 1.
%C A345132 This is the q=1 member of the q-family of sequences F_q(n), defined as the number of (n+2q) X (n+2q) symmetric matrices with nonnegative integer entries, trace 0, with n rows that sum to 2, and 2q rows that sum to 1. It is relevant to the counting of dipole graphs as is discussed in the paper whose link is given below. The q=0 member of this family is the sequence A002137.
%H A345132 Stefano Frixione and Bryan R. Webber, <a href="https://arxiv.org/abs/2106.13471">The role of colour flows in matrix element computations and Monte Carlo simulations</a>, arXiv:2106.13471 [hep-ph], 2021.
%F A345132 E.g.f.: exp(x^2/4-x/2)/(1-x)^(3/2).
%t A345132 genF=Exp[-y/2+y^2/4]/Sqrt[1-2*x-y];
%t A345132 (* seq[q,N] gives {F_q(0),...F_q(N)} for any integers q and N *)
%t A345132 seq[q_,N_]:=Table[D[D[genF,{x,q}],{y,n}]/.{x->0,y->0},{n,0,N}]
%Y A345132 Cf. A002137.
%K A345132 nonn
%O A345132 0,3
%A A345132 _Stefano Frixione_, Jun 30 2021